Tau Science Magazine 2016 by Tau Science Magazine

TAU SCIENCE MAGAZINE 2016

LETTER FROM THE EDITORS The idea of Tau Magazine was first conceived in the summer of 2015 when we were inspired by our respective research endeavors to create a science journal for our local community that is both readerfriendly and didactic. Tau Magazine hopes to foster and grow the scientific learning community at Montgomery High School, with the aim of encouraging students to share their experiences about their personal research in a laboratory setting, investigations in modern research they are passionate about, opinions and reactions to STEM related events in the high school, or anything else that helps inspire scientific spirit. There is a large variety of articles for every type of reader, including not only research and its implications in solely science, but its implications in society, daily life, culture, and even politics. This yearlong initiative has been the product of countless hours of hard work from both an administrative and a work-based standpoint. Without the help of our twenty-four writers, some of whom even submitted last minute, this endeavor would not have been possible. We would like to personally extend a huge thank-you to all those who have taken part in this new and exciting chapter of STEM life at Montgomery High School. Undoubtedly, this issue of the Tau Magazine is the first of its kind at this high school, and we are very proud of the end result. We hope that after reading the articles contained within this magazine, you have learned something new, and have hopefully even been inspired to do a little bit of your own questioning and research in a field of science that interests you. â&#x20AC;&#x153;Equipped with his five senses, man explores the universe around him and calls the adventure science.â&#x20AC;? Edwin Powell Hubble

Sofia Dimitriadoy Editor-in-Chief

Junlan Lu Editor-in-Chief

ACKNOWLEDGEMENTS BOARD OF EDUCATION Ms. Christine Witt, President Mr. Charles F. Jacey, Jr., Vice-President Mr. Richard T. Cavalli Ms. Minkyo Chenette Ms. Sandra M. Donnay Mr. Dharmesh H. Doshi Mr. Nicholas Hladick Mr. Dale Huff Mrs. Amy Miller

PTSA

Ms. Lori Huff, President Ms. Cindy Hamer, Treasurer Ms. Leslie Hauben, Recording Secretary Ms. Susan Delaney, Vice President Ms. Rania Elghazaly, Vice President Ms. Sharon Howard, Vice President Ms. Val McAlister, Vice President Ms. Christine Petrane, Vice President Ms. Lysa Wilson, Vice President

CENTRAL OFFICE ADMINISTRATION

Ms. Nancy Gartenberg, Superintendent of Schools Ms. Fiona Borland, Director of Technology Ms. Kelly Mattis, Director of Human Resources/Staff Development Ms. Mary McLoughlin, Director of Pupil Services Mr. Damian Pappa, Director of Assessment and Testing Ms. Deborah Sarmir, Assistant Superintendent for Curriculum & Instruction Ms. Annette Wells, School Business Administrator/Board Secretary Mr. Ron Zalika, Director of Curriculum

HIGH SCHOOL ADMINISTRATION

Mr. Paul J. Popadiuk, Principal Ms. Corie Gaylord, Director of Student Academics and Counseling Services Ms. Naoma Green, Vice Principal Ms. Melissa Hodgson, Supervisor of Social Studies Mr. Keith Land, Interim Vice Principal Mr. Anthony Maselli, Director of Athletics Mr. Scott Pachuta, Vice Principal Ms. Alma Reyes, Supervisor of World Languages Ms. Jennifer Riddell, Supervisor of Mathematics Ms. Karen Stalowski, Supervisor of English Mr. Jason Sullivan, Supervisor of Science Ms. Joanne Tonkin, Supervisor of Pupil Services Mr. Adam Warshafsky, Supervisor of Visual and Performing Arts

TAU SCIENCE MAGAZINE 2016

THE SCIENCE MAGAZINE OF MONTGOMERY HIGH SCHOOL

WEBSITE TAUMAGAZINE.COM

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STEM BOARD

SITES.GOOGLE.COM/A/MTSD.US/STEMBOARD

COVER ILLUSTRATION BY ANDREAS WETTERBERG

CONTENTS The Science of Flint, | 04 Michigan Angela Wang

18 | Reverse Engineering the

By the “Wear-Tue” of | 05 Technology Raghav Sambasivan

20 | The Future of Magnetism

Human Brain Ronak Rijhwani Jason Wu

20 | The Role of Plasminogen

Activator Inhibitor 1 in Airway Smooth Muscle and Asthma Ankit Shah

21 | Paradoxical Pigeon Principle Eric Jiang

22 | Civil Engineering

Applications in Science Olympiad Saba Shaik

24 | Reaching for the Stars... and Planet Nine Priyanka Dilip

25 | Spectroscopy in Astronomy Ben Yao

26 | A Mathematical Story Matthew Yuan

33 | The Leidenfrost Effect Vijay Srivastava

34 | What Makes Us All Unique Mihir Doshi

35 | What We Think We Know About Dark Matter and Dark Energy Mayank Kishore

MISC

T he S cience of F lint, M ichigan Angela Wang

Flint water compared to Detroit Water e safety and cleanliness of our water is not a topic that’s at the forefront of our minds but Flint, Michigan has taught us that it perhaps should be. Concerns about water being safe to drink first began when national news began covering the polluted water supply of the city of Flint that was given to the local community to use for nearly two years after water from the Flint River was channeled into homes and businesses through ancient rusting pipes. The water, shown to be an

ominously murky color with a sharp metallic scent, has caused developmental issues in children and anemia and seizures in adults. The Michigan government, supposed to be responsible for the health of its state’s residents, never addressed the issue, despite the fact it knew about the dangerous levels of lead in the water. The situation is all the more horrifying due to the fact that the government may have been able to neglect Flint for so long because it could ignore the pleas of the community, who was impoverished and largely from ethnic minorities. “How does this relate to science?” you ask. Good question. The heart of science thrives through not only a sense of curiosity and the desire to gain more knowledge but also the will to advance civilization and improve life for human beings. Although investigative science is often portrayed as cold and unfeeling, it actually contains a human element that aims to do the truth justice. By that logic, environmental justice, the field of regulating and enforcing environmental policies so every person regardless of race or class can live in a healthy environment free of any threats, is considered an important aspect of environmental science. Through both a scientific and political lens, one realizes how urgent the Flint, Michigan crisis is. Water that is meant to be chemically treated so it is free of any toxins has been found to contain levels of lead exceeding the standard set by the EPA, even though the Michigan government demanded for the Flint people to pay water bills; children, pregnant women, and seniors have had no choice or say about using polluted water for at least two whole years. Water pollution, thought to be only a concern in developing countries without the resources or power given to local people to demand for the government to resolve such matters, can be found right here in the United States—and furthermore, Flint, Michigan isn’t the only city impacted by contaminated water. Over 10 million homes and buildings receive water from partially lead pipes all across the country. New Jersey in fact has reported a recent crisis where 30 schools were found to have lead in the water of their water fountains. What can be done to fix the water infrastructure of America and do Americans justice by giving them safe and clean water to use? The permanent solution is replacing old pipe systems with new pipes, a solution that is both timeconsuming and costly. Legislators and scientists are banding together to use their powers to best resolve the situation in faster and more cost-efficient ways, whether it be inventing cheap filters to trap water pollutants or implementing corrosion control plans to stop the lead from entering the water. However, one of the most important solutions is to first be aware of the disturbing nature of water pollution crises in America—and demand for justice to be carried out so all can safely enjoy a resource that is meant to be a human right. ANGELA WANG 12TH GRADE

MODERN RESEARCH

BY THE “WEAR-TUE” OF TECHNOLOGY Raghav Sambasivan

gasped as Gunasekar’s ejection fraction (ef) dropped to a mere 15%. My father’s good friend, someone who always encouraged me and provided joy in times of stress, resided in India and was an avid weightlifter. When he was diagnosed with heart failure, it came as a shock to everyone. Since this process was performed at a local hospital in India, the treatment prior to surgery was not performed with recent medical equipment, which was why the depleting EF was not addressed in time. The man I admired as a health role model passed away simply because his condition was not discovered soon enough. Society is set such that thirdworld countries are held back due to inaccessible healthcare leading to millions of deaths. Thirdworld societies are known to have healthcare that is inaccessible, yet research shows that even countries that have freely accessible healthcare like Botswana, still have the highest rate of HIV/AIDS in the world. The problem is not the availability of healthcare, but rather the lack of awareness from citizens in developing nations. If everyone knew they were at risk of carrying a fatal disease, the rate of deadly epidemics in third-world countries would be guaranteed to drop. This is why the health-tracking field of wearable technology fascinates me the most, as it can provide a revolutionary solution where patients can become aware of their condition earlier, and prevent it from worsening. Wearable technology, including Google Glass, the Apple Watch, and Fitbits, are part of a booming market that dominates the world. These devices are capable of monitoring health conditions, an incredibly valuable tool for a multitude of fatal health disorders that are time sensitive. For example, if Fitbits were slightly modified to be able to detect inconsistent, or critical heartbeat rates, then they could easily

warn of arrhythmia in users and advise for a visit to their doctor. Simple device modifications are just the beginning; Google Glass could be altered to routinely examine the eye for drastic thinning or changing of shape in the cornea, the most common cause for keratoconus. Expensive yet unnecessary corneal transplantations are necessary when keratoconus is not treated early enough with corrective lenses. Simple alterations in current wearable electronics would save millions of lives and prevent unnecessary surgical operations that often waste valuable time and money. All measures described above are relatively easy to attain within a few years by simply modifying current successful devices. However, more elusive conditions such as leukemia require more extensive designs. The most efficient way to do so would be to have a wearable device that automatically transmits sound waves into the blood of the user, from which it could separate circulating tumor cells from the billions of other red blood cells. This would then report found data back to the device and provide an indication to the user if CTCs were found. An amelioration of this sort would exponentially increase the awareness of patients, and would drastically dissolve the imminent danger of the world’s most lethal disease. Obviously, this technological advancement has multiple obstacles: most saliently, third-world patients cannot afford such technology. However, this can be resolved by creating cheaper solutions with everyday devices that focus solely on health condition. Regardless, it is undeniable that the crisis of those whose conditions could have been prevented must be brought to deliberation. A situation like Gunasekar’s can finally come to an end by simply implementing this research into thirdworld locations, which is absolutely achievable through the progression of health-warning wearable technology. RAGHAV SAMBASIVAN 10TH GRADE

TAU SCIENCE MAGAZINE 2016

MHS EVENT

AMAN KISHORE 11TH GRADE

An Insight on the Impact of Monty Madness

r the past decade our Robotics team, Team 1403, has annually hosted a robotics competition called Monty Madness. Residents of Montgomery Township were welcome to watch the competition each year in an effort to increase our district’s interest in STEM related activities. FIRST Robotics Competition (FRC) is an international high school robotics competition. Each year, teams of high school students and mentors work during a sixweek period to build game-playing robots that weigh up to 120 pounds (54 kg). During each match teams have to work together with their alliance in order to score more points than the other alliance. Robots complete tasks such as scoring balls into goals, flying discs into goals, inner tubes onto racks, hanging on bars, and balancing robots on balance beams. The game changes yearly, keeping the excitement fresh and giving each team a more level playing field. While teams are given a standard set of parts, they are also allowed a budget and encouraged to buy or make specialized parts. My first introduction to robotics was when I was in the eighth grade. One evening in March, my parents brought me to a robotics competition. At first I did not show much interest in this trip as I wanted to play with my friends. As I watched the competition, this mindset was quickly dispelled. I became very interested in the game, which at the time was “Ultimate Ascent”. Watching the robots throw frisbees into goals and climbing towers made me marvel at the engineering feat that a team of high schoolers could achieve. This occasion inspired me to join the robotics team the following year. Since then my passion for robotics has elevated me to Assistant Programming Captain on the team. Last year I volunteered at our Monty Madness competition and got a chance to witness the amazing impact that robotics has had on students. Robotics is a unique competition in that there is a fair chance that one match you will be working alongside a team and the next you will be facing that same team. This cooperation and competition, or “coopertition” as FIRST calls it, gives students the opportunity to face new challenges while trying to work with what they are given. Throughout the event I witnessed students assisting their alliances and even assisting their opposition whenever a team was in need. This type of cooperation among the students was inspiring to see. Even more astounding than the cooperation was the fantastic amount of innovation and creativity I see among students. All of the robots had a unique design that best served the team. Most teams chose to focus on a few aspects of the game in order to maximize their points. The types of design elements that many teams chose to use were extremely creative. Last year’s game was “Recycle Rush” which involved picking up and stacking totes on scoring platforms, putting pool noodles (“litter”) inside recycling containers, and putting the containers on top of scoring stacks of totes. Some teams used elevators to stack the totes while others just used an arm. I believe that the most inspiring aspect of Monty Madness is the innovation that various teams bring.

When π Gets a Pie to the Face

JENNY HUANG

has become integrated in today’s society. Many of you may recognize March 14 as Pi Day. With the officially established Pi Day in 2009, enthusiasts celebrate this day by eating pie or by having festivals such as those held in Princeton. Although pi is popular in today’s society, it is facing a growing opponent—tau. Where did pi come from and how was it discovered? There is no exact date as to when the special relationship between the circumference and diameter of a circle was first noticed, but about 4,000 years ago, Babylonians and Egyptians started calculating pi. They managed to calculate this mysterious ratio with a precision up to 5 digits. Then, Archimedes came along and managed to define the upper and lower bound of pi, meaning that he deduced that pi could be no greater and no smaller than certain numbers. Afterwards, more philosophers endeavored to calculate this number, and at one point people thought that pi was equal to the square root of ten. After many years of investigations, the calculations of pi had become more exact. In the early 1700s, British scientist William Jones gave this special ratio the symbol π, and

MODERN RESEARCH not long after, the great mathematician Leonhard Euler started to incorporate this symbol into mathematics. Books, movies, and even a national holiday have been established to honor pi. Nonetheless, there are people who object the usage of pi. In 2001, University of Utah math professor Robert Palais published a short article named “Pi is Wrong,” which gives the controversy of the usage of pi. In his opening sentence, Palais (2001) states “I believe that π is wrong” (p. 8), arguing that the value of π (3.14…) should be defined as the value of 2π (6.28…) because of the prevalence of the factor 2π in numerous equations. To support his claim that 2π is more important than π, Palais lists a number of mathematical and physics equations such as Euler’s Formula, Stirling’s Formula, and Gaussian Distribution that involve 2π rather than a π. Furthermore, Palais asserts that the radius is more important than the diameter, considering how the circle is mathematically defined: “[A circle] … is defined such that all the points on the circle are at a constant distance from a center.” This constant distance is the radius. Using Palais’ reasoning, because the radius is considered more important than the diameter, the ratio between the circumference and the radius is more important than the ratio between the circumference and the diameter. The ratio of the circumference with the radius is equal to the value of 2π. Palais named the value of 2π to be 1 turn. A few years later in 2010, Michael Hartl, inspired by Palais’ “Pi is Wrong,” published the Tau Manifesto and established the first Tau Day. Hartl renamed the value of 2π with the symbol τ, tau, which comes from the first letter of the greek word τόρνος, which is the root of the English word turn. Since the launch of the Tau Manifesto, Hartl has conveyed this new idea to the public by giving Tau Talks and launching a website dedicated to tau. You may be wondering what the relevance of the pi and tau controversy is in middle school and high school studies. One of Palais’ main arguments involves a dilemma that many students face when first studying the unit circle in trigonometry. As many of you may know, there are two modes of measuring angles: the degree mode and the radian mode. The measure of an angle in radians is the ratio between the arc length and the radius. On the unit circle, one whole rotation around the circle is equal to

360°, which is equal to 2π radians. You may recognize that π/2 radian is equal to 90° and that this angle π/2 covers ¼ of the circle. In terms of tau, τ/4 rad covers ¼ of the circle. In other words, one-fourth of tau radian is associated with one-fourth of a circle while one-half of pi radian is equal to one-fourth of a circle. Many tau advocates believe that replacing tau for pi makes sense because of the simplicity that is associated with the fraction of circle and tau radians. For instance, one tau would mean one revolution around the circle, and one-half tau covers one-half of the circle.

The publication of the Tau Manifesto has not been left unchallenged. Pi enthusiasts soon wrote the Pi Manifesto to refute many of the claims against pi in the Tau Manifesto. Also, the rivalry between pi and tau does not end in the mathematical field. As pi enthusiasts celebrate Pi Day, Tauists, the name for supporters of tau, celebrate Tau Day and claim that they get to eat two times the amount of pie. The argument concerning pi and tau as well as the rivalry between Pi Day and Tau Day may be endless. However, there is a more unique day to celebrate, today1, because it is Square Root Day. In the digits of the date, 4/4/16, the first two digits are the square root of the last two digits of the year. Even rarer than the annual pi or tau days, perfect square root day only occurs nine times a century. Pie is eaten on Pi Day and two times the amount of pie is eaten on Tau Day. What is eaten on Square Root day? Square roots. JENNY HUANG 10TH GRADE

This article was written on 4/4/16 Square Root Day

TAU SCIENCE MAGAZINE 2016

select area of resin to bright white light and forming an ultrathin layer of solid on the platform (precisely 160 micrometers). 4. The variable-height platform dips another 160 micrometers deeper into the resin so that another liquid layer can flow over the previously formed solid layer. The next layer in the intended design is projected onto the overlapping liquid, which solidifies and becomes bonded to the previous layer. 5. The process of light exposure and platform lowering NICK NG is repeated until the entire design has been formed by the is summer I was fortunate enough layering of hundreds of ultra-thin solid projections of polymer. to spend four weeks at the New Jersey Governor’s Interestingly enough, assembling the printer and School of Engineering and Technology (GSET), achieving print accuracy on the scale of the several hosted on Rutgers campus. At GSET, I attended two core micrometers was perhaps the simplest portion of our classes (physics and robotics) as well as three elective courses research. Our task, as given by Professor Howon Lee, was (earthquake-resistant structures, coding with Arduino, and to use this micro-stereolithography printer as a tool to test materials science). Yet my most thorough work took place resins of various ratios of the polymers used to synthesize in my group research project, “Digital 3-D Printing of Soft it. The significance of our work was not simply to say that Robotics.” With four other scholars from all over New Jersey, we had successfully created an operating printer. Rather, it I did background research, created a 3-D printer, performed was to create a small apparatus that falls under the broad experiments, recorded data, and eventually published category of “soft robotics,” i.e. any mechanism that operates a formal scientific paper which was presented at the effectively using flexible components instead of rigid ones. conclusion of GSET and is currently uploaded on the Rutgers The resin we used had a unique property that allowed it to be used in this field, which was the School of Engineering website. Our research project “Digital I had learned far property of swelling upon contact with highly volatile solvents such 3-D Printing of Soft Robotics” more than simply as ethanol. With the knowledge dealt primarily with the use of of this property, we were able micro-stereolithography to form the mechanisms to create simple structures that semi-solid structures from liquid behind microexhibited distinct movement upon polymer (referred to as “resin”). Of the many types of 3-D printing, stereolithography contact with ethanol. A simple trench-like design allowed for the which range from simple extrusion printed design to flex when activated, not unlike how the to selective beam sintering, micro-stereolithography is perhaps the method with the most accessible basis of creation fingers on your hand curl inwards to grasp any object at will. as well as the highest potential accuracy of printing. Micro- It was this extent of “flexing” that we observed and recorded stereolithography is based on a simple mechanism; when a throughout our research, as we discovered that by altering synthesized sample of resin is exposed to bright white light, the ratio of PEG200 to PEGDA700 in the chemical synthesis a series of chemical reactions occurs that allows the resin of the resin, we could drastically alter its properties and as a to form a thin layer of solid wherever it has been exposed result, its “flexing.” PEG200 was responsible for the porous to the light (this is known as “photo-polymerization”). and highly expandable properties of the photo-polymerized To take advantage of this, only a few parts are required to prints, while PEGDA700 contributed largely to each print’s create a functional micro-stereolithography printer (small rigidity. We carefully created several identical prints of vat of resin, variable-height platform, convergent lens, varying resin ratios and compared their flexing properties mirror, and light projector connected to any computer). upon contact with ethanol to scientifically discover which Without going through the exact orientation of each ratio of polymers would make for the most effective part, the entire process is most easily described as this: material to be used for moving parts within soft robotics. 1. A layer of the intended design is projected from the By the end of my time at GSET, I had learned far more computer screen through the light projector (a given layer for than simply the mechanisms behind micro-stereolithography printing an object such as a cone would be a simple circle). and the optimal ratio of PEG200 and PEGDA700 in its The image is projected as white on a black background. resin (which turned out to be a 1:1 ratio). Rather, I gained 2. The mirror and convergent lens are positioned so that immeasurable experience with conducting formal research the light exiting the projector is redirected and focused onto a in a group. The practice of preparing a scientific paper variable-height platform which lies within the small vat of resin presentation was unlike any other, as our group shared the great so that a thin layer of resin flows over the top of the platform. motive that Tau holds—to show the world the educational 3. The layer of the design is projected onto the small capacity that scientific research has as well as the incredible amount of resin covering the platform, effectively exposing a potential that similar studies hold in the future.

PERSONAL RESEARCH

GSET IN 3D

“

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NICK NG 12TH GRADE

MODERN RESEARCH

ON PEDIATRIC STROKES SRUTI CHERUVU

want you to think of the word “stroke”. What images pop into your head? You probably see an old person with trembling hands, slurred speech, and difficulty walking. You don’t expect this kind of thing to happen to newborn babies, let alone kids and adults. But according to the Children’s Hospital of Pennsylvania (CHOP), about 3,000 children in the United States under the age of 18 per year have a stroke, and the National Stroke Association reports that “stroke remains one of the top 10 causes of death in children”. Because most people are unaware of the existence of pediatric stroke, most strokes that children and newborn babies have go unnoticed. For most children who have strokes, symptoms may include coordination problems, headache, nausea, or sleepiness. Newborns and young babies who have had strokes include seizures and eventual paralysis on one side of the body. There are two major types of pediatric stroke. A perinatal stroke can occur in a fetus during the last few months of pregnancy or when a baby is one month old. This type of stroke is harder to detect because strokes are usually recognized by their symptoms. Since fetuses are in a confined position before birth and babies are not very mobile during the first few months of their lives, they won’t be able to exhibit the same symptoms that normal stroke patients would. You obviously wouldn’t see a young baby have difficulty talking, but often perinatal stroke can be detected through subtle observations. For example, babies might only show that they had a perinatal stroke if they have a tendency to stare, twitch repeatedly, or prefer to use one side of their bodies. A childhood stroke can occur between the ages of one month and eighteen years. Unlike perinatal strokes, childhood strokes are easier to spot. This is because children who have strokes exhibit the same symptoms as regular stroke patients. However, children who have strokes exhibit additional symptoms, such as seizures on one side of the body, vision impairment, and severe dizziness. Because this type of stroke can be recognized more easily, childhood stroke patients are usually the ones that are diagnosed more quickly. However, even these obvious signs of a stroke go unnoticed, simply because most people are unaware that children can even have strokes.

TAU SCIENCE MAGAZINE 2016

Now here is the million-dollar question: what causes strokes in fetuses, babies, and children? The short answer is: for the most part, we don’t know. But we do know that the factors that put fetuses, babies, and children at risk of having a stroke are not the same as the factors that put adults at risk for having a stroke. For instance, babies, fetuses, and children are more likely to have a stroke if they have a congenital heart disorder or an infection, especially in the brain, such as meningitis. Why is it important that we talk about pediatric stroke? For one thing, just because you don’t see something doesn’t mean it’s not there. Pediatric strokes do not happen very often, but when they do, they can have debilitating effects on patients if not treated properly. It is important that these people receive the care they need as soon as possible. And the best way to do that is to make people more aware about this condition. SRUTI CHERUVU 11TH GRADE

PERSONAL RESEARCH

geothermal convection current energy savan patel

ten times, students find it hard to engage themselves in the scientific community and really put themselves out there. It isn’t always easy finding a way to experiment with ideas and may just seem too hard altogether. But, with the help of the STEM Board and the amazing opportunities that they provide to students, my group and I were able to test our creativity, knowledge, and teamwork by participating in Clean Tech Competition, a national scientific research competition. The main topic that we addressed in our research was clean, renewable energy. How could we create a form of energy that was not only efficient, but cost-effective? Today, we see all different types of technology, including hydroelectricity, solar power, hydrogen fuel, wind power, and

geothermal energy. So, we had to try and devise a method of energy conversion that would utilize a new source of energy. Consequently, we began looking in the world around us for examples of energy and eventually came up with the idea of controlling convection currents, which are the circular kinetic movement of fluids due to differences in density. More specifically, our system used the natural and renewable geothermal energy of the earth to heat a container of air that would then in turn rise due to a difference in temperature. A pipe would centralize that flow of air so that we could increase the potential energy. At the top of the pipe, there would be a fan-like object to help convert that wind energy into electrical energy which could be used to power several items. The basic idea behind our model was that other systems that utilize geothermal energy don’t actually convert that energy into electrical energy, but instead transfer the heat itself. Another form of energy that is currently in use is underwater wind farms that take energy from the ocean currents—so we wanted to combine these two ideas and create it on a small-scale level. At first we wanted to see how water would act as the fluid, but we eventually realized with the help of Montgomery High School physics teacher Dr. Chao, that air would be a better fluid for our purposes. So, after several hours of research, we came up with a model. In order to see the effectiveness of our model, though, we created a prototype that used a hot plate as its source of energy. Fortunately, we were able to successfully create an air flow that could theoretically spin a turbine. But with any experiment there are always complications, and our group came across a fair share of problems. One of these problems was finding a turbine that had the right shape and weight in order to maximize the amount of energy produced. That problem is a complication that we are still trying to resolve and that is just one of the parts of the scientific process. In the end, we have learned that mistakes can lead to success and we are continuing to work at our project to make it the most successful it can be. SAVAN PATEL 9TH GRADE

MODERN RESEARCH

Controlling Carbon Dioxide

David Zhang

now, most people are aware of the worsening climate change. Recent summers have been breaking record temperatures, one after another. Ecosystems are being destroyed all over the world, and volatile weather has become the norm. The earth is deteriorating due to our actions; not only do we pour countless tons of pollutants into the air, but we also contribute to other aspects of the damaged environment. Deforestation, mining, and almost anything industrial can lead to the direct destruction of local habitats and ecosystems, on top of producing pollutants as a byproduct. With all this in mind, I started doing research on something that could change the world. It wasn’t long before I came across something that fit the bill: carbon capture. We all know that carbon dioxide is bad for the air and is considered a greenhouse gas. Carbon capture is a process in which carbon dioxide is taken from the air, and is either stored or repurposed for another use. Sounds amazing, right? Well, it’s not actually that useful—at least for us everyday people. You see, carbon capture is really only useful for point source pollution, which is a specific location from which pollution is being released. So in reality, only places like factories can make use of carbon capture. Even if everyday people could capture carbon dioxide easily, we probably wouldn’t know what to do with it. When factories capture carbon, it’s usually coupled with something called “sequestration”. Sequestration is basically the process of storing carbon dioxide in such a way that it cannot affect the air. Usually, the factories end up pumping it into the ground, either into depleted oil reservoirs or really deep beneath the earth, where it can’t escape into the air. Like I said before, carbon capture is great and all, but everyday people can’t utilize it. However, upon doing some research, there might be a way. Over the years, significant progress has been made on using

TAU SCIENCE MAGAZINE 2016

ion exchange to capture carbon dioxide from the air— known as air capture. By coating a piece of plastic with an anionic resin, researchers were able to pull out carbon dioxide from the air and onto the resin. In simpler terms, this substance contains anions; in the case of carbon dioxide, hydroxide ions (OH-). These hydroxide ions attract carbon dioxide molecules to form bicarbonate (HCO3-), thus taking carbon dioxide from the air. Pretty incredible stuff—but it gets better. When the anionic resin gets wet, something called “moisture swing” occurs, and the resin releases the carbon dioxide by replacing it with the moisture. An idea that professors had was to place the exhausted—meaning having already absorbed carbon dioxide—resins into a moist greenhouse. The moisture would release the carbon dioxide, and the plants would use up the carbon dioxide. However, we obviously wouldn’t be able to do this with the tons of carbon dioxide in the air, and we would probably have to resort to the aforementioned storage techniques that are used in an industrial setting. Despite its current limitations, it’s still an incredible solution to dealing with carbon dioxide in the air. Right now, a big factor affecting the viability of air capture is cost. Most speculate that it will never be affordable for everyday use, but a few professors believe it’s possible. As you can see though, this technology has the potential to change the future and more people should be aware about the potential it holds. The more people aware of this technology, the greater chance of becoming viable it has. Obviously, carbon capture isn’t the be-all and endall when it comes to pollution reduction. Carbon dioxide is only a fraction of the pollutants plaguing the environment. However, if carbon capture can be widely implemented, it could definitely slow down climate change and buy both humans and the earth a lot of time. DAVID ZHANG 10TH GRADE

P o l i t i ca l “S c i e n c e ”

Nidhi Kapate

MISC

our current Congress, out of 535 to derive data, not just understand it—they can identify representatives and senators, only 19 are physicians, discrepancies and sometimes revolutionize them into new 2 are scientists, and 0 are engineers, while the concepts, an especially helpful tool for policy making. remaining 514 are a mix of lawyers or business owners. At Politicians often employ different rhetorical methods first, this seems to make sense when you consider that lawyers and both Republicans and Democrats inflate statistics, are the ones specializing in law and legislation. Thus in manipulate numbers, and distort the opinions of experts. theory, they should be the ones maximizing the effectiveness The inclusion of scientists and engineers in government of our government. But you only need to look at the current would not sway favorably towards one party over another. In presidential election to see that that’s not always the case. fact, the political leanings of those with a science background We need more scientists and engineers in government. range all across the spectrum, with engineers tending to More than half of all economic growth over the past be more conservative than scientists. These new voices 100 years can be attributed to technological advancement that are experts in different areas than present politicians and many of the serious problems that our would serve to only enhance the conversation government faces today have some basis it is often occurring in the government. In fact, in in science or technology. Scientists and 2010, Representative Bill Foster, a physicist, engineers are the ones who can provide considered came up with a negative feedback filter plan the most accurate information and reliable that would prevent future bubbles in the to be opinions on many integral issues. And housing market—a plan that was applauded this is something that other nations have ‘career by economists all across the board. But learned. In China, 8 out of 9 of the top when this noteworthy solution was actually suicide’ government officials are scientists or introduced to Congress, it fell on deaf ears engineers, including President Xi Jinping, to take an and did not make it past the theoretical stage. with the same ratio existing throughout While scientists and engineers would be a extended favorable the rest of the country’s government. contribution to politics, the reason German Chancellor Angela Merkel has a that they aren’t already has to do mainly break doctorate in chemistry and in Singapore, with how their careers are structured. While President Tony Tan has a doctorate in mathematics. studying in fields that are competitive and constantly Yet nothing like this is found in the United States. developing, it is often considered to be “career suicide” to At a time when America is losing its place at the take an extended break and return with the expectation of forefront of science and technology, it’s imperative that not having been severely penalized for your absence. This is a scientists and engineers play a larger role. While scientists problem that there is no obvious solution to yet, but a potential serve as advisors to government officials, oftentimes their one is for research institutions, tech corporations, and the input travels through multiple sources and is distorted rest of the science industry to specifically reserve positions so in order to be appear more favorable for a political those who run for or hold office have jobs they can return to. agenda. Instead, they need to be an actual, present part The fact still remains that with scientists and engineers of the discussions that are happening on Capitol Hill. more involved in politics and working as elected officials, our Aside from being experts in their respective fields, country would be making more effective progress in reclaiming scientists and engineers possess unique skill sets that our place on the cutting edge of science and research. It’s time they have been able to refine and master—among which that the current rhetoric shifted from “Does global warming are risk assessment, logic, and creativity (contrary to exist?” to “What is the most cost-effective way of harnessing popular belief, science is a very creative discipline). wind energy?”. The only way that we can advance as a society Scientists especially have the unique skill of being able is if we advance our appreciation and regard for the sciences.

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NIDHI KAPATE 12TH GRADE

MHS EVENT

“The Wild and Wacky World of Epigenetics” Reflection Vicki lu

“The Wild and Wacky World of Epigenetics” was a lecture given by Professor Shirley Tilghman at the Princeton Plasma Physics Laboratory on January 19, 2016 as part of its Science On Saturday program series.

www.enzymlogic.com

biology class, we learned a lot about Mendel and his impact on modern genetics— namely, his famous pea plant experiments and rules on inheritance. Basically, Mendel observed a 100% green offspring generation (F1) arise when he crossed homozygous yellow and homozygous green peas. This proved that even though all plants in the F1 generation were hybrids, and thus inherited both a yellow and a green allele from the parental generation, the green allele was dominant over yellow, causing all the hybrid plants to appear green. Since Mendel, many new concepts have arisen about the theory of inheritance, including the much more recent theory of epigenetics.

TAU SCIENCE MAGAZINE 2016

Simply compared, in genetics, there is a change in the sequence of DNA, whereas in epigenetics, there is a change in the packaging of DNA. For example, in maize, the green plant doesn’t have the pigment the purple plant does, so when a homozygous green and homozygous purple are crossed, you’d expect the hybrid F1 generation to appear purple. However, this is not the case, as all the hybrid children actually appear green. A closer look into the DNA sequence shows that there’s nothing wrong with the allele inherited from the purple parent because they’re good copies—it’s just being “silenced,” or not expressed. How is this possible? What causes this difference in expression?

VICKI LU 11TH GRADE

Jarrett Perkins

Starting from the basics, we know that DNA is never free floating; it is actually tightly packaged through multiple levels until it becomes a chromosome. Now it starts to get a little more complicated—the degree of packaging can change within cells. On euchromatin, the packaging is loose, causing regions with high transcriptional activity (let’s refer to this as gene “ON”/open). On heterochromatin, the packaging is dense, causing regions with little to no transcriptional activity (gene “OFF”/closed). So now that we’ve learned what this phenomenon is and how it works, how can it be applied to the real world? Professor Tilghman touched upon epigenetics in cancer, social castes, and even human traits like obesity. It’s theorized that cancer doesn’t completely arise from mutations, but rather is a result of epigenetics as well. In normal cells, there are two tumor suppressor genes that are both expressed, but mutations and mis-packaging during the development of a cancer cell cause no gene to be expressed at all. This mispackaging of genes that slow down growth further contributes to the development and spread of cancer cells. Epigenetics is also seen in how social insects generate different castes. For example, when a hive needs a queen, a bee will be fed a specific diet of royal jelly whereas worker bees are fed worker jelly. The result is a queen bee much larger in size than the worker bees; both bee types have the same DNA sequence, but royal jelly changes the way characteristics are expressed. Behavior of parents can also affect the epigenetic programming of offspring such as when offspring have a greater likelihood of obesity if their parents were obese. Because we know all these different ways the field of epigenetics affects our world, we can start to develop ways to use epigenetics to our benefit. With the example of obesity, we understand that lifestyles can be passed down. If we can pass down unfavorable traits like obesity, why shouldn’t we be able to pass down favorable lifestyle traits to our children? With the example of bees, we understand that certain substances can alter the expression of genes. Why not spend time to find substances that humans can take to alter the expression of their genes? Instead of using substances to only treat the epilepsy symptoms of Angelman Syndrome (an epigenetic disease), why not find substances to fix the root cause of the syndrome itself? And lastly, with the example of cancer applications, we learned packaging or mis-packaging is a crucial element to genetic expression. Again, instead of treating symptoms, we should be working on methods to make densely packed “closed” chromatins containing genes, such as the tumor suppressors, “open”. I could be completely wrong about the concepts behind these extensions, but regardless, the experience was more important because I loved how eye opening this lecture was as it connected a unit we learned inside the classroom to a current field in the outside world.

SCRATCH PROGRAMMING CAMPS

MHS EVENT

PERSONAL RESEARCH

n fact: according to the Bureau of Labor Statistics, by 2020 there will be 1 million more computer science jobs than computer scientists in the United States. With this deficit in mind, an increasing number of organizations are popping up with the goal of engaging young children and teaching them the fundamentals of coding. This past summer Anooj Lal, a Junior at Montgomery High School, and I set out to see whether we could draw upon our prior programming experiences and utilize them to teach others. To provide some background, I gained my first exposure to programming my freshman year, when I began following the Harvard CS50 lectures. From there my learning progressed to other online resources and various classes, as well as a great deal of experimentation on my own. However, all of these experiences can be attributed to my earliest exposure to coding, the one that truly peaked my interest and pushed me to delve further into the subject area, that being Scratch. Scratch is an open-source software developed by MIT and designed to teach children fundamental coding concepts in an environment that is both fun and educational. In its most basic form, it is simply puzzle pieces that users can drag and drop and fit together to build small programs. However, Scratch is much more powerful in that it allows students to learn important ideas central to programming in a way that can be understood and followed by people of all ages. It teaches students how to form logical statements, how to utilize variables, even how to test for certain conditions. Its use of colloquial language makes it incredibly accessible to young children and as a result, is an amazing learning tool. For the reasons described above, there was no question that Scratch would be the platform through which Anooj and I would teach the kids. From there we took on the difficult task of establishing our camps. In this aspect we struggled from the start, being turned down by many potential venues, often out of hesitation due to our age and experience level with teaching. But we found a partner and an incredibly helpful resource in our county’s local library system, where we ultimately ended up holding our camps. The connectedness of the different libraries in the Somerset County Library System afforded us the unique opportunity of holding multiple camps and reaching a much larger group of kids. However, this necessitated that Anooj and I take

on other instructors, as we did not have the time nor the resources available to teach all of the camps on our own. Instead, we selected seven other instructors from Montgomery to aid us in our teaching endeavors. In the weeks leading up to the start of the camps, we worked to train the instructors, teaching them all that they needed to know about Scratch, while also providing them with curriculums and various projects to lead the kids through. By the time the first camps started at the end of June, our instructors fully understood Scratch and some had even developed a genuine interest in programming, asking for further opportunities to continue their learning (our first taste of teaching success). While Anooj and I did teach one camp ourselves, the experience of overseeing the other camps offered an entirely different set of challenges. From Wi-Fi troubles, to genuine flaws in the curriculum, our camps were not without error. However, with each session, the kids grew more and more engrossed in their work, many taking home their projects and continuing them outside of class. As we worked out the kinks and revised the curriculum, things ran more smoothly and every camp culminated in success, smiles, and hopefully some future computer scientists. As overseers we were forced to problem solve, but as teachers we were forced to learn. Teaching involves incredible communication skills and patience, and while it’s something that sounds like common sense, it’s actually much more difficult in practice. Over the course of our camps, I learned that a misunderstanding, an error in the code, or a lost student were rarely the fault of the students themselves. Miscommunication is in fact the fault of the communicator, in this situation the teacher. Being forced to reevaluate everything I said, every analogy, every comparison that I felt made the material easier to understand, was difficult, but it ultimately yielded amazing realizations and learning on my own behalf. In breaking down concepts into their simplest form, I learned things and achieved a level of understanding I previously had not possessed. That summer Anooj and I ran a total of 5 camps, reaching over 75 students in the Somerset County area. Whether we truly inspired any of our students to become programmers and pursue computer science in the future is yet to be known. However, in the act of teaching, we learned profound lessons ourselves— lessons we will continue to apply as we expand our camps and our mission in the next couple months.

overseers “Aswe were forced to problem solve, but as teachers we were forced to learn.

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JARRETT PERKINS 11TH GRADE

TAU SCIENCE MAGAZINE 2016

MODERN RESEARCH

THE CARS OF THE FUTURE

IVAN CHAU

ing Electric Vehicle in Science Olympiad, I’ve had the opportunity to see many different designs and structures of an electric vehicle. From super well-built vehicles with intricate wiring to moving pieces of cardboard, I’ve seen a lot of ways to do the event. With the serious developments in the electric car industry, I’m excited for the future. This year and in 2015, we’ve seen self-driving vehicles, cars that can pull themselves out of garages, and the expansion of affordable electric vehicles to the consumer market. With the competition between Tesla, BMW, Audi, and other motor vehicle leaders heating up, we can only expect things to get better for consumers worldwide, and electric cars to grow in prevalence as well. With advances, the opening scene from The Incredibles is almost a reality. The technology used to build these cars today involves a mixture of artificial intelligence (AI) scientists, engineers, computer scientists, and data scientists. Today, vehicles like the Tesla Model S learn how you drive and make the world a safer place by putting driver data into a large worldwide database. This database is used by the rest of the consumers who also drive a Tesla. For example, lets take Somerville Circle for instance. It’s pretty close to a driver’s nightmare, even though I’ve never personally driven on it myself. Lets say you’re in “self-driving” mode and your car takes the opening turn too wide. You take control of its self-steering so it doesn’t end up driving into traffic. The next time you take the curve, again in “self-driving” mode, the car slows down a bit by itself and slowly takes the curve. It’s learning, using AI. By the next time you take it again, the

car hugs the curve perfectly. The car uploads this to a huge database of driving data. After a software update, your friend, who’s not such a great driver takes the same curve in selfdriving mode. It perfectly takes the turn—but only because you drove it and the car learned it first. This can have enormous effects, as the number of drivers increase, this road data will spread across the country. In this way, electric vehicles are becoming more and more important by aiding driver safety and by lowering carbon emissions. This might not seem like a lot, but AI has empowered cars to work flawlessly by learning and taking statistics on roads all over the country— all from everyday driving of other fellow consumers. AI science has become so important as it enables a machine to learn by itself. This can even be seen in Super Mario World as a machine learns how to complete each level by itself by testing button combinations, much like how the human brain learns (and wins, after 34 tries). Even more recently, AI programmers have designed a program that plays the board game Go. After playing professionals, it learns playing styles and has become an unbeatable program. With this technology in everyday vehicles, this can have a huge impact on the future of electric cars. Elon Musk, CEO of Tesla who recently released “summon,” a feature in which a press of a button allows your car

MHS EVENT MODERN RESEARCH

to driver-lessly drive to your location, quoted in a tweet that:

SCIENCE FOR THE FUTURE ANEESH ATRI

Hypothetically, with all the user data across highways and backroads, your car could drive itself cross-country, refueling at charge stations for free and without the burden of finding a place to sleep and everyday dangers of driving. This also has several applications for the everyday life— whether it be calling your car after exiting a supermarket because you forgot where you parked it, or even calling your car from a restaurant out from street parking because it’s way too cold outside. All of this was made possible with artificial intelligence and Tesla’s consumers. With all this technology and development over a short period of time, it’s not such a crazy prediction to say that we won’t need driver licenses within a decade. Cars drive themselves, they can parallel park, and they can enter and leave garages, all with the use of a smartphone. Vehicles are becoming more like computers than just vehicle transports. They get software updates over-the-air, with no USB connection needed. This means you can wake up with new features you’ve never seen before. With growing research in alternative energy, electric efficiency, and artificial intelligence, it’s becoming more environmentally friendly, cheaper, and easier to drive. And cars are starting to look really cool—and, in time, affordable. Even at competitions at Science Olympiad, competitors use circuit boards like Arduino to program and have the car make decisions (independent of user inputs) with rotation sensors and light sensors, to achieve the desired distance to the nearest centimeter if needed. With the youth being inspired by companies like Tesla, BMW, and Audi, who are driving advances in the automobile industry, it is not so difficult to see the interest in artificial intelligence and data science escalate to high numbers as more and more people become inspired. And, as a student, I feel more inclined to learn these things myself—the progress of these companies have me motivated me to achieve the same. IVAN CHAU 9TH GRADE

That’s the number of people who currently use the Internet. This is approximately 39% more people compared to 1995. It is quite clear that the human race becomes more and more dependent on technology to perform certain tasks, whether it is typing up your homework, searching up a statistic, or even watching a video. Technology has advanced far more than just this. Experts believe that technology can outsource jobs that were once done by humans. One such profession that has been outsourced by technology is that of bank tellers. Prior to the digital age, there used to be an abundance of bank tellers. Every time someone would visit a bank, they would visit the teller to withdraw money, but now, there are ATM machines that can perform 85% of the tasks bank tellers used to do. Of course, not everyone aspires to be a bank teller, but the idea is that technology will someday outsource certain jobs and the people making this technology will benefit from it. Science is important for this reason because we are going to need it even more in the future. Even now, robots are able to perform certain surgical procedures with more precision, flexibility, and ease compared to the conventional surgery tactics. It’s only a matter of time before this technology improves and expands. However, one key aspect that machines lack is the human brain. Perhaps the brain’s greatest skills are its ability to make connections and to create and innovate. People need to start taking more of an interest in science because we need to stay ahead of the curve. We cannot afford to have unemployment in this country and we also need to create machines that can solve problems that we as humans have failed to solve.

40%

ANEESH ATRI 9TH GRADE

TAU SCIENCE MAGAZINE 2016

MODERN RESEARCH

Reverse Engineering The HUman Brain

Ronak Rijhwani

Brain visualization data by John Van Horn (US), Neda Jahanshad (US), Betty Lee (US), Daniel Margulies (US) and Alexander SchĂ¤fer (DE). 20

MODERN MODERN RESEARCH RESEARCH

What if “ we could

instead create a precise replica of the brain in the form of a super computer?

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pidly progressing into a new era characterized by technological innovation, society has utilized revolutionary discoveries in science to benefit its people in a multitude of ways. As of today, there exist cars that possess the capability to drive themselves to increase road safety and ease, 3D printers that can fabricate organs for surgical implants to better human health, and man-made rice plants that can undergo “supercharged photosynthesis” for more efficient farming and poverty reduction. Such advancements that start with a mere idea extend beyond knowledge to a tangible impact on our world. Computational neuroscientists today are currently trying to bridge this gap between knowledge and impact by developing a model that replicates the functions of the human brain with the hope to better human health. Our current understanding of disease, medicine, and psychology is dependent on experimentally supported hypotheses regarding how the human brain reacts to independent factors (e.g. disease, external stimuli, etc.). But what if we could instead create a precise replica of the brain in the form of a supercomputer that serves to accurately predict the response the human brain is wired to have based on a set of rules? To almost anyone new to this idea, the initial response is skepticism based on the fact that the human brain is not a computer program; it does not follow a set of rules that can be inputted into a computer. However, while this is true to some extent, the brain does use many simple rules to solve highly complex problems, and extracting each of these rules one by one could lead to the model neuroscientists have longed for. For example, research has found simple design principles that allow billions of neurons to connect to each other in almost the same

patterns (person to person) depending on the location of those neurons. The brain’s response to a needle poked on the tip of one’s right thumb will be almost identical to the subsequent response when the same needle is poked in a similar manner ten minutes later—that is, the firing of a similar amount of nociceptors (pain receptors) follow almost exactly the same neural pathways to report to the thalamus. Of course, this is dependent on a multitude of factors, such as the person being poked, the needle’s sharpness, the pressure applied on the thumb, etc. Taking all these factors into consideration makes it understandably challenging for scientists to implement such variables into a single accurate model of the brain that can respond to an almost infinite number of stimuli. Despite the seemingly insurmountable task, Professor Henry Markram of the Brain Mind Institute in Switzerland is highly optimistic that modeling the human brain can become a reality. “I absolutely believe it is technically and biologically possible. The only uncertainty is financial. It is an extremely expensive project and not all is yet secured,” stated Markram. If we can reverse engineer the brain as Markram says, then we can input data to make milestone discoveries in medicine, physcology, and disease. For example, by programming a model brain with a specific cancer cell and attempting to eradicate those cells through different hypothetical biomedical stimuli, one could potentially create an effective treatment for that cancer using the model brain. If this idea proves to be true, whether it is ten years from now or a thousand, and a replica of the human brain created with a set of programed rules is successfully created, the understanding we have in the field of computational neuroscience becomes more than knowledge—it becomes an impact on the way we live. RONAK RIJHWANI 10TH GRADE

TAU SCIENCE MAGAZINE 2016

Jason Wu

THE FUTURE OF MAGNETISM

PERSONAL RESEARCH

gnetism is a phenomenon that continues to enhance nearly every aspect of human life. Magnetic resonance imaging (MRI) uses magnetic fields to construct meticulous images of human organs, playing a crucial role in medical research. The Japanese High Speed Surface Transport (HSST) system utilizes electromagnetic levitation in order to improve transportation. Magnets even directly affect human transactions of currency on the back of credit cards in the form of magstripes. Although magnetism already strongly influences our lives today, its effects will become further ingrained into society through the future discovery of room temperature superconductors. Superconductors are objects that can conduct electrical current without any form of electrical resistance, meaning no energy is lost. On an atomic level, resistance occurs because electrons collide with conductor particles causing energy loss. However, when conductor particles are at rest, electrons can pass through without collisions, eliminating resistance. The conductor is then said to be a “superconductor”. Superconductivity is a very difficult phenomenon to utilize practically. As described before, in order for a superconductor to operate, its particles must be stagnant so that electrons can easily move through them. Thus, most superconductors have to be cooled to exceptionally low temperatures to function. Although this immense temperature obstacle has restricted practical implementation of superconductors for some time, improvements are continuously being made. Initially in 1911, Dutch Physicist Heike Kamerlingh Onne discovered that mercury exhibits superconductivity at around 4.19K,

a temperature close to absolute zero. However, in 1986, IBM researchers K. Alex Müller and George Bednorz discovered high-temperature superconductors among ceramic materials, which could superconduct at temperatures up to 138K above absolute zero. Though much has improved from the temperature requirement observed by Onne in mercury, ceramic superconductors still exhibit large flaws. Liquid nitrogen must be used to cool these ceramic materials, meaning a refrigeration agent must still be present. They are also exceptionally difficult to physically mold into components like wires. Thus, in order for superconductors to be fully implemented into society, scientists must find an easily moldable material that still exhibits superconductive properties without the presence of external cooling. If such a superconductor is discovered in the future, it will augment development in multitudinous engineering fields, particularly transportation. Maglev trains are vehicles that hover above magnetic rails. By placing magnets in a repulsive orientation on both the track and the bottom of the vehicle, the Maglev train floats. This eliminates friction between the vehicle and the track and consequently increases speed. Maglev technology has gained popularity in countries such as Japan and China, where train use is very common. The reason this transportation technology has not proliferated in other countries is cost. Maglev vehicles and tracks are very expensive to create and maintain. Future discoveries of cheap room-temperature superconductors would greatly alleviate this issue by providing a simple way to generate large magnetic fields. Breakthroughs in superconductive materials would also assist medical technology enhancements. MRI’s are currently very bulky and expensive. Cheap superconductors would be able to reduce the size of MRI machines by replacing nonuniform magnetic fields. The field of magnetism will ultimately substantially increase in influence following the discovery of room-temperature superconductors. JASON WU 10TH GRADE

The Role of Plasminogen Activator thma is a widespread disease, affecting Inhibitor 1 in over 300 million people in the United States. It is a complex disease that is most commonly As characterized by chronic inflammation and airway remodeling, Airway Smooth the combination of which results in the observable difficulty to breathe. Present medications include inhaled corticosteroids, Muscle and which research now suggests can have detrimental effects on Consequently, research has turned towards finding Asthma Ankit Shah patients. other pathways to target with pharmaceuticals. Airway smooth 22

MODERN RESEARCH

ERIC JIANG

PARADOXICAL PIGEON PRINCIPLE

‘

st of you have probably heard of the Pigeonhole Principle before. If you have not, here is a short introduction: the Pigeonhole Principle was discovered in 1834 by Peter Gustav Lejeune Dirichlet, a member of the Prussian Academy of Sciences. He imagined having sixteen pigeons and fifteen pigeonholes. If a storm were to come and the pigeons needed to take shelter in the pigeonholes, there would be a variety of ways in which they could be placed in the pigeonholes; all pigeons could stay in one hole, or a specific number of pigeons could be assigned to a select number of pigeonholes. This situation led Dirichlet to formulate what he called the Box Principle. It said that if “N” number of pigeons were placed into “N – 1” number of pigeonholes, there would always be at least two pigeons in one hole. The logic of Dirichlet’s principle seems intuitive and simplistic, yet it can be used to solve seemingly difficult problems that initially appear to have no relation to it. For example, the pigeonhole principle can be used to show that if a chess board were to have two diagonally opposite squares removed, it would not be possible to cover the board with dominos that take up the space of two adjacent board squares. This is because diagonally opposite squares are of the same color. If the two white diagonal squares were removed, the board would be left with 30 white squares and 32 black squares; the number of squares of one color would exceed the number of squares of the other color by two. This relates to the Pigeonhole Principle in that each domino takes up the space of two adjacent board squares, which means that it establishes a 1:1 ratio between the set of white and black squares. Thus, if the two colors had a different number of squares, then by the Pigeonhole Principle, it would not be possible for a 1:1 correspondence to be made. At the end of this example, two non-adjacent black squares would be left uncovered. However, recently, this principle has met opposition in muscle (ASM) cells are the primary cells responsible for the tightening of the airway via contraction. Their role in the pathogenesis of Asthma has become increasingly important as a possible target for new, safer medication. Plasminogen Activator Inhibitor 1 (PAI-1) prevents the conversion of Plasminogen into its active form of Plasmin, which contributes to inflammation as well as build-up of the Extracellular matrix, both of which cause serious problems for the cell. PAI-1 is produced in large amounts by Mast Cells, which are immune cells, and are the main inhibitor of the important fibrinolytic system. However, its role in asthma remains unknown. My research looked at PAI1 specifically in ASM. Using western blotting TAU SCIENCE MAGAZINE 2016 to determine the

fields such as quantum physics. Yakir Aharonov, among other physicists, experimented with three particles and two boxes. He conducted pre-selection measurements, intermediate measurements, and post-selection measurements to measure the position of the three particles simultaneously. This led him to find that there were situations in which there are more particles than boxes, but no more than one particle in each box. As a result, this quantum conundrum has led many physicists to revisit the basic notions of quantum physics: separability, correlations, and interactions. It also provides deeper insight into entanglement as well as other quantum processes. The violation of the Pigeonhole Principle has led to a reexamining of, and greater understanding in, many subsections of quantum physics. In contrast, current and ongoing experiments are revealing that quantum-interference effects can make it appear that each box only holds one particle, even though two particles might actually be present. A proposed experiment to test the violation of the Pigeonhole Principle involved sending three electrons through an interferometer, which would split the electrons from one path to two. The three electrons would then be brought together at a second beam-splitter before diverging to two different detectors. By the Pigeonhole Principle, if there are three electrons and two paths at the interferometer, at least two electrons must stay on the same path. This would mean that those two or three electrons on the same path would be close enough to repel each other, leading to their trajectories being affected. However, with current technologies, these distinctions are extremely difficult to detect. The effect that each electron has on the other is so miniscule, that the results appear similar to if there was only one electron in each path. Despite its origins in 1834, the Pigeonhole Principle has continued to affect modern theories and work because it is a fundamental principle that captures the essence of counting and relates to many other fields in mathematics and science. ERIC JIANG11TH GRADE

protein expression levels, various treatments were added to both asthmatic and nonasthmatic cell lines. Basal expression, TGFbeta induction, siRNA-mediated serpine1 gene knockout, as well as various Cytokine treatments were all used to determine the role or roles of PAI-1 in ASM. It was found that Asthmatics have lower basal levels of PAI-1 than do Non-asthmatics in ASM; however, TGF-beta, which also promotes collagen secretion, induces PAI-1. Lower basal PAI-1 levels would result in more Plasmin and thereby chronic inflammation, and higher PAI-1 would cause more ECM buildup. Further research may elucidate a possible pharmacological application for PAI-1. ANKIT SHAH 12TH GRADE

MHS EVENT

CIVIL ENGINEERING APPLICATIONS IN SCIENCE OLYMPIAD SABA SHAIK

ience Olympiad gives students an opportunity to learn about a wide range of topics that are not covered in our science curriculum. There are around twenty “events,” or subjects, we can compete in, from study-based events like Astronomy to hands-on building events like Electric Vehicle. The variety of material can be a really interesting supplement to what we learn in class and introduce us to new areas of science that we would never have thought to explore otherwise. Out of the many events I’ve tried in Science Olympiad, my favorite by far is Bridge Building, in which the objective is to build the lightest possible bridge that can also support the greatest

(which occurs when two forces act on a part of the bridge in opposite directions), tension (which pulls on the wood), and compression (which pushes down). Since we aim for bridges with small masses, we have to create designs without superfluous “members,” or pieces of wood. Every member in a bridge needs to serve a specific purpose, therefore in our design process we need to consider how each individual member contributes to the structural integrity of the bridge as a whole. Some of my rough sketches are shown in Figure 2, with forces color coded and labeled (just compression and tension, since the diagrams only include one side of the bridge). In design 1, for instance, all the load is distributed on the two side members. They are pushed down and out, so they are under compressional stress, while the bottom member is under tensional stress because it pulls the side members in to prevent them from collapsing outwards. Our bridge building process can be broken down into three loose steps. The first is to find a design that works fairly well but also has potential for improvements. Then we modify it, paying more attention to the mass that the bridge

Fig 2 mass. The largest allowable mass to load a bridge with is 15 kilograms, but there are no mass restrictions on the bridge itself. Scores, or “efficiencies,” are calculated by dividing the mass that the bridge held by the mass of the bridge (both in grams). Our materials are limited to balsa wood and glue. There are a lot of stringent design parameters that we need to follow, but the most important ones to keep in mind are that the bridge must span 45 centimeters, one side must be raised by 5 centimeters, the other side has a 2 centimeter height limit, and the top must accommodate a loading block which is attached to a bucket containing some mass that can be gradually poured, usually sand. Figure 1 depicts a typical testing apparatus. The physics behind Bridge Building are not complicated, but are very important to understand while designing and building. Four main forces control how weight is distributed among the components of the bridge: moment (the torque or twisting of each side of the bridge), shear

can support rather than the mass of the bridge itself, and aim to build one that can support the entire fifteen kilograms. Once this is accomplished, we focus on making the bridges lighter, which is generally the most difficult part. Mass reduction can be done in a few ways: using lower density balsa, thinner balsa, less glue, or removing unnecessary members. Finding a balance between substantially cutting down a bridge’s mass and maintaining its strength is tricky and can involve many rounds of experimentation. The reason why we haven’t settled on one design, and perhaps the reason why we see such a huge variety of them at competitions, is that every design has unique advantages and no single one is fundamentally better or stronger. In my opinion, how well a bridge bears a load really depends on how well it is built. That said, I am impressed by one design in particular; our “Illuminati” (Fig 3) started as a joke, but since we tested the first one, it has consistently produced Fig 1

Fig 5 Fig 6 record-breaking efficiencies. We reasoned that the top arch behaves as another compression member while the two in conjunction act somewhat like a spring that supports large loads while retaining some elasticity in the bridge. Figures 3 and 4 show a few more of our high scoring designs. I especially like Bridges because it gives us some insight into the responsibilities of civil engineers and what goes into building the actual bridges that we use every day. The process of constructing real bridges is of course much, much more

Fig 7 Fig 8 points to ensure they are safe and durable. Often bridges collapse as a result of unexpected torsion and oscillation, like winds or earthquakes, rather than from heavy loads. I think one of the most interesting aspects of bridge construction—and one that has been a source of countless intuitive engineering solutions—is how bridges are constructed over large bodies of water. First, a foundation, usually made out of concrete, has to be laid in preparation to support the “superstructure,” or the main part of the

Fig 3 complex and intensive than building our 5 gram balsa wood models. Our testing apparatus is always the same whereas actual bridges are built to last in a variety of natural conditions. Civil engineers need to collect a huge amount of information before even starting their designs. Some factors to consider include plans of the site detailing any obstacles for the bridge to subtend (rivers, valleys, streets, etc.), requirements for the bridge (width of lanes, walkways, traffic directions, medians), the topography of the environment, weather conditions, local surroundings, and safety concerns. Usually, several plans are drafted and compared before choosing one based on its merit in strength, market appeal, and manufacturability. Figure 5 shows a portion of the plan for the Chicago and Alton Railroad Bridge1. Actual construction involves huge projects that encompass several engineering disciplines including geological, electrical, mechanical, and computer sciences. Building bridges is a long and costly process that takes several years and usually billions of dollars. Once this is done, they have to be tested with different loads and reinforced at certain

Fig 4 bridge. There are a few ways to do this: 1) a foundation can be built on land or on top of the water, and then sunk down (Fig 6); 2) less frequently done, rigs can be employed to drive piles, or long steel or concrete poles, into soft beds of soil until they reach the bottom of a body of water. This is known as a pile bridge (Fig 7); and 3) more commonly done, cofferdams are prepared, which are walls enclosing a dry building area where water is constantly pumped out. The foundation is then built inside the cofferdams (Fig 8)2. Superstructures can be built in many ways. If you want to observe an example of building over water, check out the construction of the Tappan Zee Bridge over the Hudson River in New York. The original Tappan Zee bridge was built in 1952, but is being replaced with a modern one because its existing structure is deteriorating—it has to bear much more traffic per day than it was intended for and it was designed to last for only 50 years. Construction of the new bridge started in 2013, and it is scheduled to open in 2018.

SABA SHAIK 11TH GRADE

Bridge Engineering.” About Civil. WebTechTix, 2014. Web. 2 Row, Jayant R. “Bridge Construction.” Bright Hub Engineering. Bright Hub Inc., 2015. Web. 1“

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PERSONAL RESEARCH MODERN RESEARCH

Reaching for the stars... and Planet Nine Priyanka Dilip Ga zing up into the sky. Watching the intricate dance of celestial bodies. No, I’m not speaking of the planes flying overhead, but of a world far beyond that—the world of astronomy. Looking at colorful pictures of nebulae and supernovas always instilled this curiosity, this yearning in me, to know how such colossal structures formed. In a way, the entire field of astronomy is really mankind’s awestruck exploration of how and why processes at unimaginable scales created us, along with stars and galaxies and even dark matter! Sure, physics, biology, or mathematics have that similar kind of precise allure to them, but none can even approach the scale, the power, or the fierce beauty discovered in the universe through astronomy. So in this exploration, the theoretical discovery of a Ninth Planet, a possible long unknown relative in our solar system, is one of the rewards that astronomers earn for being just a little more out-of-this-Earth than everyone else. The “Ninth Planet” symbolizes our need to find more worlds like ours, a need that countless scientists have been trying to satiate since Pluto was demoted to dwarf planet status in 2006. Along with satisfying those who mourned the loss of Pluto from the solar system’s planetary elite, Planet Nine has resolved some significant anomalies in the observed motions of objects in the Kuiper Belt. And we needn’t worry that our latest Planet Nine, when discovered, might be stripped of its Planet status, for its mass is predicted to be 5,000 times the of Pluto and thus it gravitationally dominates an area far larger than any of the existing eight planets. Six of the most distant objects in the

Kuiper Belt follow elliptical orbits that are inclined in the same direction —30° downward from the plane of the eight known planets’ orbits—even though they move around the solar system at different orbital velocities. This is where the magic of computer models comes in—the two scientists simulated a system where a massive planet moved in an antialigned orbit relative to the six Kuiper Belt objects and the eight known planets. The results? The simulation data amazingly corresponded with the actual motion of the Kuiper objects! Through mean-motion resonance, Planet Nine distorts the six objects’ orbits to have the properties described above. The gravitational effects of the proposed Planet Nine’s orbit also help explain unusual Kuiper Belt objects that never approach Neptune, unlike others. However, one of the most solid proofs for the two scientists’ theory has been the exact correlation of a second set of Kuiper Belt objects. In this case, Planet Nine’s orbits predicted the existence of objects orbiting the solar system at right angles to the eight known planets’ orbital planes. Five objects have been discovered to date that exactly match the predicted perpendicular orbits! Each of these correlations proves more strongly that there is a Planet Nine out there, perfectly fitting into the modern definition of a “planet,” ready to be discovered, explored, and one day even visited! This is what makes astronomy so exciting—the sheer exhilaration and awe that strike the observer’s mind and leave one passionate to explore more.... PRIYANKA DILIP 10TH GRADE

MODERN MODERN RESEARCH RESEARCH

Spectroscopy in Astronomy

Ben Yao

r sun is composed of mainly hydrogen and helium. The question is, however, how do scientists know this and what did they do to discover this? How do scientists know what stars and other objects in space are made out of without samples from those stars or objects? The answer to these questions lie in the science of spectroscopy. The science of spectroscopy pertains to the measurement of electromagnetic radiation that is emitted by certain objects. In astronomy, scientists use spectroscopy to analyze the absorption and emission lines emitted by objects such as dust clouds, stars, and other deep space objects. When light emitted by these objects is passed through a spectroscope, it is split into its component colors: red, orange, yellow, green, blue, indigo, and violet. Light from these objects, however, usually does not come out as a perfect spectrum and they often have dark or bright lines in them which can reveal the traces of elements that are present in those clouds/stars. Astronomers are able to use these methods to detect elements present in stars because in most stars, the outer layers of the stars are cooler than the inner layers and when a star’s light passes through the gaseous outer layers, the atoms or ions of the elements that are contained in the outer layers absorb the energy (photons) emitted by the inner core of the star. These atoms absorb energy that is equal to the difference in any two of their energy levels and this causes their electrons to move from their ground state into an excited state. Once the excited state is reached, the electrons eventually lose their energy and fall back into ground state and emit energy that is equal to the difference in energy levels that the electron travelled. The wavelength of the photons emitted by the atoms in the

star’s outer layers are unique to the element(s) present in that specific layer, but they never reach the spectroscope because they are emitted in a different direction. Because of this, these wavelengths appear as dark, missing, absorption lines on a continuous spectrum. By examining these dark lines, we can determine what elements are present in stars. Furthermore, astronomers use spectroscopy to find the elements that are present within nebulae or clouds. Instead of reading absorption lines, however, astronomers read emission lines— bright lines that appear on a dark spectrum. When a nebula or cloud is heated up by something such as a star, the atoms of the elements present in the nebula become excited and the electrons of the atoms move from ground to excited state. After the electrons fall back down from excited to ground state, they release energy in the form of electromagnetic radiation which is then detected by a spectroscope and shown as a bright lines on a dark spectrum. In addition to being able to discover the types of elements present in stars, spectroscopy can also be used to approximate the age of stars. For instance, if a star’s spectra contains traces of iron, then an astronomer can conclude that the star is a very old and large star that is nearing its death—it is most likely a red supergiant. Iron in a star’s spectrum correlates to old age because iron is extremely hard to fuse and is so tightly bound that it does not produce enough energy to sustain the star so fusion stops once iron-56 is reached. As a result, the old star ends up with an iron core which will be unable to balance out the inward pull of the star’s own gravity, and depending on its mass, the star will quickly collapse into either a black hole or a neutron star in the near future. In spectroscopy lies the answers to many puzzling questions in astronomy. By using techniques like the ones above, astronomers are able to detect both the approximate age, type of star and elements found within stars, and other deep space objects. Because of spectroscopy, astronomers have gained vision and knowledge of even the furthest places in space and are now able to advance the future of astronomy just by interpreting the images on a spectroscope. BEN YAO 10TH GRADE

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“A Geometer’s Secret” Alberto J. Almarza, 11 Novemeber 2011 Fractal trees, platonic solids, sphere, geodesic triacontrahedron and other geometric objects. Created by hand using compass and straightedge. Graphite, tea and wax on paper.

MISC

A MATHEMATICAL STORY Matthew Yuan

Questions or corrections? Email me: matthewfelixyuan@gmail.com

1 Prelude: The Greeks

Ancient Greece was home to lots of mathematicians who studied geometry. From the Greeks we get the Platonic solids, Heron’s formula, the Pythagorean theorem, and from a man named Euclid, we get compass-andstraightedge constructions.

Eukleides of Alexandria (“Euclid” to his friends)

In the 300’s BC, Euclid wrote the Elements, where (among other things) he developed the kind of geometry that deals with shapes drawn using only an unmarked straightedge and a compass. The foundations of Euclid’s geometry (which mathematicians have so imaginatively named “Euclidean geometry”) are his five postulates: 1. It is possible to draw a straight line from any point to any other point. 2. It is possible to extend a line segment continuously in both directions. 3. It is possible to draw a circle with any center and any radius. 4. It is true that all right angles are equal to one another. 5. It is true that, if a straight line falling on two straight lines make the interior angles on the same side less than two right angles, the two straight lines, if produced indefinitely, intersect on that side on which are the angles less than the two right angles.

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MISC Starting with these postulates, Euclid logically concluded lots of other facts, which he called propositions. Some propositions state a property of some shape or construction, like Proposition 5, Book I. The base angles of an isosceles triangle are equal.1 The propositions we will focus on, however, are those that describe methods to construct certain shapes, specifically, regular polygons. One such proposition is Euclid’s very first: Proposition 1, Book I. To construct an equilateral triangle on a given line segment, draw the two circles centered at the endpoints of the segment with radii equal to the length of the segment.

Reading through the Elements gives the impression that it’s really difficult to come up with these constructions. Euclid gives methods to construct a triangle, a square, a regular pentagon, a regular polygon with 15 sides, and then... regular polygons are never mentioned again. Given that there are infinitely many regular polygons, it’s hardly an achievement to construct four of them. Thankfully, there’s another proposition that can be used to construct many more: Proposition 9, Book I. Bisecting angles is a thing you can do.2 The fact that you can bisect an angle means that if you’re given a regular polygon, you can bisect its central angles and get a regular polygon with twice as many sides:

Bisecting the central angles of a square gives the vertices of a regular octagon.

From triangles, squares, pentagons, and 15-gons, angle bisection gives you hexagons, octagons, decagons, and 30-gons. You could bisect the angles as many times as you wish, and you would get dodecagons, 16-gons, 20-gons, 60-gons, and so on. A full list of the numbers n where a regular n-gon is constructible from methods presented in the Elements starts out like this: 3, 4, 5, 6, 8, 10, 12, 15, 16, 20, 24, 30, 32... To make the list more general, I’ll restate it with some variables, and to make the list more official-looking, I’ll typeset it like a theorem: Regular polygons with constructions known to the Greeks. A regular n-gon has a construction known to the Greeks if n is in one of the following forms, 2k, 3•2k, 5•2k, 15•2k, where k is a whole number. Now this list looks a whole lot better; from our four starting polygons and angle bisection, infinitely many regular polygons can be constructed! However, the list is still incomplete. None of the Greeks had been able to construct regular heptagons, or nonagons, or 11-gons, or many, many others. This bothered them a lot, to the point where they put the construction of these polygons on their list of Totally Stupid3 Problems: Angle trisection. To split into three equal parts a given angle. Squaring the circle. To construct a square with an area equal to that of a given circle. Mystery polygons. To construct regular polygons with the number of sides 7,9,11,13, etc. Doubling the cube. To construct a cube with a volume double that of a given cube. The real frustrating part of these problems was that geometers weren’t even sure that solutions existed.4 The Greeks struggled over these problems for centuries, yet they remained unsolved. As time went on, mathematicians lost interest and moved on to other things. Maybe the circle just needs to be big enough to flail your arms and legs inside it...

This proposition has a funny Latin name which I will leave for you to discover. Euclid probably wouldn’t have phrased it that way, and probably would’ve given the explanation as to how exactly one bisects an angle, but I’m trying to keep this article short, so I’ve omitted it. You can check out the method to bisect an angle, as well as the constructions for the regular square, pentagon, and 15-gon, here: bit.do/snakesonaplane 3read: unsolved 4“Maybe constructing a regular heptagon is impossible! Or maybe we’re just not clever enough to figure out how.”

MISC

2 30 March 1796

Two math students walked through the meandering paths around the University of Göttingen campus. The man with longish hair and a broad face was Farkas Bolyai, and the one with short hair and sharp features was Carl Friedrich Gauss. They walked in silence, each occupied with their own thoughts.5 It was like most days, until the moment when Gauss decided to say something. “It’s possible to construct a regular seventeen-sided polygon.” “Wait, what?” Nobody, not even Bolyai, really knew what went on in Gauss’s mind. He had the habit of keeping these ideas closely hidden, then suddenly producing theorems out of thin air. “You know, a compass-and-straightedge construction.” “Of course I know, but nobody’s discovered anything new about Greek geometry since, well... the Greeks!” Bolyai had experience in these matters because for much of his career he studied Euclid’s fifth postulate. Everybody thought postulate #5 was way too complicated, and suspected it could actually be proven from the first four. Centuries of mathematicians later, no one had found such a proof.6 Gauss was only nineteen years old, but he had already proven the fundamental theorem of algebra, created a new notation for modular arithmetic, and demonstrated the law of quadratic reciprocity.7 And now this! Bolyai thought. “How do you know it’s possible?” “Yes, well I think the idea most people don’t see is that not all geometry problems are about geometry.” “Um... I don’t understand.” “It’s just that—hmm. Let me show you then.” They went over to a nearby bench as Gauss pulled out his diary. He adopted what Bolyai referred to as his teaching face: a confused, wrinkled frown quite unlike his usual serene expression. Despite his mathematical adeptness, Gauss was not much of an educator. Bolyai had seen Gauss’s attempts to be a tutor, which usually ended with him giving up and proclaiming something like Can’t you see? The answer is right there! Look how beautiful/clever/obvious it is! to some crying first-year student. For some reason though, Gauss always found Bolyai worth the effort. “A regular seventeen-sided polygon, or heptadecagon, has a central angle of radians and looks something like this...”

“Wha... how did you draw that so accurately?” “Practice,” Gauss responded, as if sketching heptadecagons was something one simply practices, “but my drawing skills are besides the point.” “Okay, so how do you properly construct one?” “For a start, you have to decide how big of a heptadecagon you would like.” “Let’s say I want one with a radius this long—” and Bolyai drew a line segment. “That’s a fine radius. I’ll mark this endpoint as the center O, and I’ll mark the other one as a vertex A. Furthermore, I’ll define the length of this segment to be 1. Could you take this compass and construct for me the circle of radius 1 that’s centered at O?” “Alright... there.” “Because every vertex of the desired polygon is a distance 1 away from the center, all the vertices lie on this circle. Now pretend for a moment that you know how to find the point on segment OA that is a distance cos away from O. I will again approximate...

Once you’ve found this point X, you can draw the line perpendicular to segment OA that passes through X, and it will intersect the circle at some point B. Since the length of segment OB is 1, the angle AOB is , so B is another vertex, and the segment AB is one side of the heptadecagon. Erase everything except A and B, and then you can find the remaining vertices by using the compass to mark off lengths equal to AB all around the circle. Connect the vertices and you’re done.” Bolyai nodded as Gauss was connecting the last few

Historical sources indicate that Gauss and Bolyai did go on such walks, so in a sense this story is based in fact, but the dialogue is entirely fictional. 6 Bolyai’s son would later show that the fifth postulate isn’t even necessary, and that other weird (but perfectly selfconsistent) geometries exist in which the fifth postulate is false (a realm that mathematicians have so creatively named “non-Euclidean geometry”): bit.do/hyperspace 7 There’s a Wikipedia article entitled “List of things named after Carl Friedrich Gauss.” And it has a table of contents. 5

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MISC

Bolyai started to see where this was going. “Hmm, you can solve this equation by making use of de Moivre’s identity, (cosx + isinx)n = cos(nx) + isin(nx) Set n = 17 and then look for all values of x such that nx equals some multiple of 2π. Let’s see... the roots are cos0 + isin0, cos + isin cos + isin ,

...

sides. “I bet the hard part is constructing that segment OX.” “Your suspicions are correct. In general, segments that have lengths expressed with sine and cosine aren’t constructible, but—” “Definition of constructible?” Bolyai often had to jut in and make Gauss clarify the words and phrases he invented for himself. “Ah yes, the definition of constructible is... um... something I should elaborate on.” Gauss flipped back some pages. “Here’s a fact the ancient Greeks didn’t take advantage of...” The constructibility theorem, part 1. Given a unit segment, you can use a compass and straightedge to construct any segment whose length is a quadratic surd. “Definition of quadratic surd?” “A number expressible using only integers, addition, subtraction, multiplication, division, and square roots. For is a quadratic surd, while the example, the number number π is not.” “Okay, but I don’t see why this theorem is true.” “The details of the proof are unimportant to the 17-gon construction in particular, but I believe I wrote a summary of the proof in here somewhere... here it is. You may read over it if you wish: bit.do/gaussnotes” “Oh I see now. You’ve reduced proving that the regular heptadecagon is constructible to proving that a line segment with length cos is constructible, and by this theorem, cos is constructible if it is a quadratic surd. But how do you prove that? Is there some trigonometric identity that could be useful here? Hmm... cos = cos2 — sin2 , which means—” “No, you cannot just focus on that! Knowing how to construct cos is sufficient to construct the regular heptadecagon, but it’s not enough to really understand how it behaves. You should be looking at the regular heptadecagon as a whole and figuring out how it’s special, what properties it has that might lead you to the conclusion that it is constructible. Only thinking about cos is to study the works of Monet by staring at the individual paint strokes.” “I guess that makes sense... wait who’s Monet?” Gauss, realizing too late that Impressionism hadn’t been invented yet, replied quickly, “Ummm, never mind that. The point is, we’re going to study the regular heptadecagon in its entirety. Right, so, um, let’s do that. Yes. Can you think of an equation that connects all the vertices of a regular heptadecagon together?” Bolyai began calculating slopes of linear equations. Monet? Is that French or something? “Oh no, I meant an equation that describes the vertices. I meant the equation z17 = 1. The solutions to this equation are the 17th roots of unity, and when graphed on the complex plane, the roots look like seventeen points spaced equally on the unit circle...”

cos

+ isin .

That cos shows up again in the second root, because the real part of a complex number represents that number’s x-coordinate in the complex plane. What’s next?” Gauss was in the midst of writing down a large sum of terms. “Yes, that’s correct...” he replied offhand. “Hey!” Bolyai took his pencil. “Mmm, yes?” The rest of the world came back into focus. “What was the point of that? Representing the vertices as roots of unity didn’t do anything! The roots are still in terms of trigonometric functions!” “That is merely because you used the straightforward method to find them.” “What?” “If we try to hunt for each root individually, as you have done, all we get are solutions in this form with cosine and sine. We will instead solve for the sum of all the roots, then slowly break it up into smaller and smaller sums until we’re left with individual terms. In this way, we’ll be able to see their true quadratic nature.” “Enlighten me.” Gauss drew out a new diagram. “First, we’re going to get rid of these trigonometric descriptions. Just call this root here r. Then the next root (by de Moivre’s identity) is r2,

MISC and the next one is r3, r4, and so on, until you’ve gone all the way round the unit circle to r17, which we can write in a simpler way, because r17 = 1. The set of roots is now written as {1, r, r2, r3, . . . , r15, r16}.”

“Okay, done.” It took two pages of algebra to turn out this ugly thing, x2 — (r16 + r15 + r14 + r13 + r12 + r11 + r10 + r9 + r8 + r7 + r6 + r5 + r4 + r3 + r2 + r)x + r30 + r29 + r28 + 3r27 + 2r26 + 2r25 + r24 + 3r23 + 3r22 + 3r21 + 4r20 + 4r19 + 4r18 + 4r16 + 4r15 + 4r14 + 3r13 + 3r12 + 3r11 + r10 + 2r9 + 2r8 + 3r7 + r6 + r5 + r4 = 0. “You are not quite finished.” “What do you mean?” “We know the value of the x-coefficient, remember? Also since r17 = 1, any power of r greater than 17 can be reduced to a power of r less than 17. For example, r18 = r, r30 = r13+17 = r13 • r17 = r13, 414 r = r6+17(24) = r6 • (r17)24 = r6.” Bolyai raised a skeptical eyebrow. “I don’t think that’s going to help much, but I’ll try it...” Another three minutes and four seconds. “Wait. How... is that possible?!”

“Fair enough.” “Right from the start we know the sum of all the roots. Because they are radially symmetric, the sum of all the roots 3 How It’s Possible must be zero, “All the roots have imaginary parts! How did all of that 16 15 14 13 12 11 10 9 8 7 6 5 4 r +r +r +r +r +r +r +r +r +r +r +r +r suddenly disappear??” Bolyai stared at his result, scrawled + r3 + r2 + r + 1 = 0.” quickly at the bottom of the page, “That’s true, but it doesn’t tell you anything about the 3 10 5 11 14 7 12 6 9 13 15 values of each term in the sum. How are you going to break (x — (r + r + r + r + r + r + r + r ))(x —(r + r + r + r16 + r8 + r4 + r2 + r)) = x2 + x — 4??? the sum apart?” Gauss made the kind of grin that says I told you so. “All “Actually, there is one trivial8 root whose value we the roots react with each other and fizzle away until nothing do know: 1. We can remove it from the sum by simply remains except integers. Do you see the solutions to the subtracting it out, equation now?” 16 15 14 13 12 11 10 9 8 7 6 5 4 r +r +r +r +r +r +r +r +r +r +r +r +r Eyes widened in epiphany. “You can just use the + r3 + r2 + r = -1. (1) quadratic formula! The solutions to x2 + x — 4 = 0 are Look at what we have now! Sixteen terms? Quadratic surds? Sixteen is a power of two? So that means...?” and , “Um, what?” “The remaining sixteen roots can be split into two sums and because the quadratic formula only uses addition, subtraction, multiplication, division, and square roots, the in a very particular way, solutions are quadratic surds!” r3 + r10 + r5 + r11 + r14 + r7 + r12 + r6, “Precisely. Although it appears that the two sums of r9 + r13 + r15 + r16 + r8 + r4 + r2 + r, roots must be complex numbers, they are in fact real and the value of these two sums can be determined if you , and the other is . numbers. One sum is let them be the solutions to a quadratic equation, Can you tell which one is which?” 3 10 5 11 14 7 12 6 9 13 (x — (r + r + r + r + r + r + r + r ))(x — (r + r “Can I draw something?” + r15 + r16 + r8 + r4 + r2 + r)) = 0. “Of course.” Can you solve this equation for me?” “Um... What is there to solve? The equation’s already in factored form.” “Expand it.” “Really? That’s pretty much the opposite of solving a quadratic equation.” “I know. Expand it.” Bolyai sighed. It was getting dark. Ten minutes and twenty-eight seconds later. r3 + r10 + r5 + r11 + r14 + r7 + r12 + r6 r9 + r13 + r15 + r16 + r8 + r4 + r2 + r 8 Mathematicians like to call results that aren’t difficult to prove “trivial.” They tend overuse it, to the point where physicist Richard Feynman noted, “There are only two types of theorems: the trivial and the unproven.”

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MISC “Drawing out all the roots, I see that you chose both sums so that they’re symmetric across the x-axis, which is why they are real numbers. The sum of all the roots on the left looks negative, and the sum of all the roots on the right looks positive, so that means r3 + r10 + r5 + r11 + r14 + r7 + r12 + r6 =

(2)

r9 + r13 + r15 + r16 + r8 + r4 + r2 + r =

(3)

I’m guessing you have a magical way to split these sums in half and solve-by-expansion again?” “Indeed I do. Consider the equation (x — (r9 + r15 + r8 + r2))(x — (r13 + r16 + r4 + r)) = 0, whose solutions are r9 + r15 + r8 + r2 and r13 + r16 + r4 + r, two halves of the sum in equation (3). By expanding, the equation becomes x2 — (r9 + r13 + r15 + r16 + r8 + r4 + r2 + r)x — (r16 + r15 + r14 + r13 + r12 + r11 + r10 + r9 + r8 + r7 + r6 + r5 + r4 + r3 + r2 + r) = 0, and from equations (1) and (3) we can further simplify to x2 +

(

)x + 1.

This time we have a coefficient that is the solution to a previous, larger-sum equation.” “I got it from here.” Bolyai took Gauss’s pencil again. After a bit of algebra and inspection of the diagram, he found r13 + r16 + r4 + r = r9 + r15 + r8 + r2 = “Once again, just an application of the quadratic formula, so nothing more complicated than square roots was necessary. Is it possible to just keep going like this?” “I believe so. Give me a moment to write everything out. (16, 3) = r3 + r9 + r10 + r13 + r5 + r15 + r11 + r16 + r14 + r8 + r7 + r4 + r12 + r2 + r6 + r (8, 3) = r3 + r10 + r5 + r11 + r14 + r7 + r12 + r6 (8, 9) = r9 + r13 + r15 + r16 + r8 + r4 + r2 + r (4, 3) = r3 + r5 + r14 + r12 (4, 10) = r10 + r11 + r7 + r6 (4, 9) = r9 + r15 + r8 + r2 (4, 13) = r13 + r16 + r4 + r (2, 3) = r3 + r14 (2, 5) = r5 + r12 (2, 10) = r10 + r7 (2, 11) = r11 + r6 (2, 9) = r9 + r8 (2, 15) = r15 + r2 (2, 13) = r13 + r4 (2, 16) = r16 + r Here are all the sums, along with some abbrevations. The abbreviation (n, k) describes the sum of n terms that contains the rk term. Using this notation, the whole list of equations is (16, 3) = -1 (x — (8, 3))(x — (8, 9)) = x2 — (16, 3)x + 4(16, 3) (x — (4, 3))(x — (4, 10)) = x2 — (8, 3)x + (16, 3) (x — (4, 9))(x — (4, 13)) = x2 — (8, 9)x + (16, 3) (x — (2, 3))(x — (2, 5)) = x2 — (4, 3)x + (4, 9) (x — (2, 10))(x — (2, 11)) = x2 — (4, 10)x + (4, 13) (x — (2, 9))(x — (2, 15)) = x2 — (4, 9)x + (4, 10)

(x — (2, 13))(x — (2, 16)) = x2 — (4, 13)x + (4, 3) (x — r3)(x — r4) = x2 — (2, 3)x + 1 (x — r10)(x — r7) = x2 — (2, 10)x + 1 (x — r9)(x — r8) = x2 — (2, 9)x + 1 (x — r13)(x — r4) = x2 — (2, 13)x + 1 (x — r5)(x — r12) = x2 — (2, 5)x + 1 (x — r11)(x — r6) = x2 — (2, 11)x + 1 (x — r15)(x — r2) = x2 — (2, 15)x + 1 (x — r16)(x — r) = x2 — (2, 16)x + 1 From this you can see that the solutions of the equations in one group can be used to find the solutions of the equations in the group below. Since we know the value of (16, 3), we can (albeit tediously) solve the equations all the way down, halving the groups each time until we get to individual roots. Only at that level do the solutions get imaginary components. Since the entire process is the repeated solving of quadratic equations, the solutions are guaranteed to be quadratic surds, and therefore guaranteed to be constructible. If I did the algebra right, then the value of the real component of r, which is cos , should be cos

“Woah. That’s a bit much to take in all at once. I guess I can see the general idea, but how the heck did you choose those special sums? And why are the terms in that weird order?” The teaching face caught hold again. “A satisfactory answer to your questions would be long and complicated, but if you really must know, perhaps we can discuss it another time. It has become too dark to see my notes; perhaps we should be heading back.” bit.do/morenotes

4 The End

The following publication appeared in the April 1796 issue of the Allgemeine Literaturzeitung. It is known to every beginner in geometry that various regular polygons, viz., the triangle, tetragon, pentagon, 15-gon, and those which arise by the continued doubling of the number of sides of one of them, are geometrically constructible. One was already that far in the time of Euclid, and, it seems, it has generally been said since then that the field of elementary geometry extends no farther: at least I know of no successful attempt to extend its limits on this side. So much more, methinks, does the discovery deserve attention... that besides those regular polygons a number of others, e.g., the 17-gon, allow of a geometrical construction. This discovery is really only a special supplement to a theory of greater inclusiveness, not yet completed, and is to be presented to the public as soon as it has received its completion. Carl Friedrich Gauss, Student of Mathematics at Göttingen

GRAPHIC In 1801, Gauss published Disquisitiones Arithmeticae, a huge collection of his various mathematical works, including his aforementioned theory of greater inclusiveness. The theory showed the constructibility of all polygons whose number of sides is a prime number one more than a power of two. Such numbers are called Fermat primes, and Gauss listed a few, 21 + 1 = 3, 22 + 1 = 5, 24 + 1 = 17, 28 + 1 = 257, 16 2 + 1 = 65537. Gauss ended his list there because he didnâ&#x20AC;&#x2122;t know of any others. To this day, no other Fermat primes have been found. Gauss considered the discovery of the contructibility of these polygons to be one of his greatest acheivements. He wanted a regular heptadecagon inscribed on his tombstone, but it wasnâ&#x20AC;&#x2122;t done because the engraver said it would look just like a circle. However, a small seventeen-pointed star can be seen at the base of a statue of Gauss in his home town of Brunswick.

You can make your very own heptadecagon by following this method first described by the mathematician Herbert William Richmond in 1893, almost a hundred years after Gauss proved it to be constructible: mathworld.wolfram.com/Heptadecagon.html

THE LEIDENFROST EFFECT Vijay Srivastava

Illustrated here is one of my favorite physical phenomena, the Leidenfrost Effect. When water is poured on a hot skillet, it logically should vaporize almost immediately. Instead, something interesting happens. As soon as the water hits the skillet, the bottom layer of the droplets turns to vapor. This vapor creates a cushion underneath the drops of water, which bead up due to surface tension. As a result of the Leidenfrost Effect, the water rolls around the skillet in drops rather than boiling off. Vijay Srivastava 11TH GRADE

MATTHEW YUAN 11TH GRADE

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MODERN RESEARCH

WHAT MAKES US UNIQUE Mihir Doshi

eryone is unique. Whether it be interest, hobbies, self-perception, or behavior, each individual has at least one defining characteristic, something which distinguishes them from those around them. Although people generally tend to accept that they are unique and even take it in a positive way, others often ponder over why they aren’t the same. They look at others around them, and often feel they are “not as good” in comparison. These individuals fail to understand that they are not better or worse than those around them, but that they are only different. After all, everyone has their own unique aspects that differentiate them from others. Even after these individuals realize that they are different, they crave to know why they are dissimilar. In short, everyone is different and possesses their own unique qualities because of their brain. Scientifically speaking, the brain is an organ of soft nervous tissue contained in the skull of vertebrates, functioning as the coordinating center of sensation and intellectual and nervous activity. In simpler terms, the brain is what determines what a person does, how they move, how they perceive the real world, their emotions, etc. The brain is hugely interconnected, but four major components can be identified. These include the cerebrum, the brainstem, the hippocampus, the medial temporal lobe, and the cerebellum. The cerebrum, by far, is the largest part of the brain. It makes up 75% of the brain by volume and 85% by mass. Divided by the longitudinal fissure, which is a large groove, the cerebrum is split into two distinct hemispheres—the left hemisphere and the right hemisphere. “Left” and “right” refer to the owner’s point of view, not an outsider’s point of view. The two hemispheres are linked by a large bundle of nerve fibers called the corpus callosum, and also by other smaller connections called commissures. In general, the left hemisphere controls the muscles on the right side of the body. It is also dominant in language, particularly in processing what you hear and handling most of the duties of speaking. The left hemisphere is also in charge of carrying out logic and exact mathematical computation. When you need to retrieve facts for a test, your left-brain will pull it from your memory. Your right hemisphere, on the other hand, controls your muscles on the left side of your body. This hemisphere controls face recognition, as well as your perception of visual imagery and music. Mathematically, it can perform some rough estimates, but it cannot derive exact values like the left hemisphere. The brainstem controls involuntary actions such as breathing, digestion, and your heart rate. For example,

if an individual is exercising strenuously, the brain stem will tell the heart and lungs to increase the pulse rate and breathing rate respectively. The brain stem also connects the rest of the brain to the spinal cord and the lower body. The hippocampus is essential for memory, particularly transferring memory from short-term to long-term. It is also in charge of controlling spatial memory and some aspects of behavior. Unlike other parts of the brain, the hippocampus is capable of growing new neurons. However, this ability is impaired depending on stress and hormone levels. The medial temporal lobe, located

between the left and right hemisphere, essentially controls declarative and episodic memory. In other words, this part of the brain controls what many people refer to as a “photographic memory”. Finally, the cerebellum plays an important role in balance, motor control, and fine motor skills. It is also involved in some cognitive functions such as attention, language, emotional functions such as fear and pleasure, and in the processing of procedural memories. For many doctors and surgeries, the cerebellum is what helps them recall how to perform an operation. Thus, it is evident that the brain is an extremely complex organ. It consists of several different parts, each of which acts in different ways from one person to another. It is ultimately the human brain that makes every individual unique. MIHIR DOSHI 9TH GRADE

MODERN RESEARCH

What We Think We Know About Dark Matter and Mayank Kishore Dark Energy

ems like a made up thing. Everyone has heard of regular matter and energy. Matter is a substance that occupies space, and energy is the capacity of an object or a particle to do work. So what is dark matter and dark energy? Isn’t that found somewhere in the Star Trek franchise? Why is it called dark matter? Why have scientists been confounded by the known but unknown implications of dark matter and energy? Although it does seem to fit under the category of science fiction, and it still may, there is increasing evidence that dark matter and dark energy are intrinsic properties of the universe, and not in a negligible

Some of the universe’s gamma rays, seen here in five years of data from the Fermi Gammaray Space Telescope, could be produced by proposed dark matter interactions.

fashion. Dark matter and dark energy are said to encompass 95% of the universe. These are baffling concepts that stump even the greatest minds. Hopefully this article will allow for the first step to understand space, just a little better. Everyone knows that matter is a physical object that takes up space and contains mass and that energy is simply the ability to do work. What most people don’t know is that this matter only makes up a small fraction of the matter in the entire universe. In fact, it is said that the visible universe made of matter only makes up 5% of the entire universe. The rest of the universe is held together by, what we have dubbed, dark matter and dark energy. The only problem in proving that it exists is that dark matter and dark energy are invisible. Even so, scientists are sure that dark matter and dark energy exist. Let’s start with dark

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matter and what we know about. We know that the gravity of the visible matter is clearly not strong enough to form galaxies and more complex structures. Without dark matter, there would most likely exist stars that are scattered all over the place as there would not be sufficient force to hold these galaxies and solar systems together. These large and complex structures depend on dark matter to hold their shapes. The conundrum with dark matter is that it does not emit or reflect light and therefore is invisible to our eyes. Our only sound reasoning behind the existence of dark matter are places with high concentrations of dark matter. At these places there is something that interacts with gravity. It is also known that most of the matter in the universe is dark matter, not regular matter. Galaxies never would have formed in the first place had not the gravity generated by dark matter gathered primordial materials together when the universe was young. Dark energy is even more mysterious due to its effects on the universe. It is intrinsic to space itself and keeps getting stronger. Astronomers believed that the expansion of space would be slowing down as a result of gravity. Instead, the complete opposite was occurring! Distant supernovae showed that a long time ago, space was expanding at a much slower rate. This lead to the conclusion that the expansion of space had not been slowing down, it had been speeding up! Theorists coined the term dark energy to explain what caused this rapid expansion. An interesting theory behind dark energy is that space is actually full of “virtual particles” that are constantly created and destroyed. Unfortunately, this was quickly disproven due to the fact that the amount of energy from such an occurrence would create an amount of energy too immense to ignore. Scientists believe that space may act more like a dynamic fluid in order to account for such vast amounts of energy. It is said to account for 68% of the universe. The clear complication is that such an immense sum of energy would not be able to hide in space. It would be interesting to find out what dark matter and dark energy really are as it would help expand the realm of physics and answer many questions. Clearly dark matter should not be ignored—though it tries very hard—and should be studied to allow for complete understanding. The conundrum with both dark matter and dark energy is that, at the moment, we have no idea how to verify its existence. Hypotheses have been made for the properties of dark matter and dark energy, but without proof, it will never become an accepted truth. MAYANK KISHORE 11TH GRADE