@creativetallis www.thomastallis.co.uk www.creativetallis.com tallismanifesto.weebly.com
A TALLIS FANZINE
PIZZA MATHS Instead of just eating pizza, Sang and Precious decided to apply some simple measurements, and found themselves a bargain. Words: Precious John
Buying a pizza is something most people enjoy doing for a variety of reasons, and value for money is the most important thing to consumers the world over. This cautionary tale is a great example of doing the maths before you buy. I was walking with Sang in Woolwich one afternoon, when we stumbled on this hidden pizza place that would change our view of bulk-buying. We went into the restaurant and ordered a 15” pizza and five 7” pizzas, each of which cost £5 pounds. The idea of this ridiculously cheap pizza was so mind-boggling we decided to apply some simple maths. Measuring the radius of the 15” pizza and of the 7” pizzas we calculated the area of each size pizza using the formula A=r2 and found that the 15” pizza had a smaller area than that of 5 x 7” pizzas. This was mind blowing. The ultimate test was determining the quality of this amazingly cheap pizza. So we sat down and had what would be the best buffet of our lives because it was apparent that this magic pizza was rich in quality, quantity and value for money which really is a dream come true for any shopper, buyer or hungry person.
Life -Sized Tetris
create a solid line. In a maths lesson last month we scaled up each piece of the cube and stuck them together to make the sections. This culminated in us creating a giant robot figure as tall as the walkways by slotting the pieces together without gaps between them. It was essentially one massive, outsized Tetris game.
Who said maths lessons consisted of someone droning on about equations? Not at Tallis, where we made Soma cubes instead. Words: Ben Linden
The Soma cube was invented in 1933 by Danish polymath Piet Hein. It consists of seven pieces which combine to make a cube of equal height width and depth, similar to those featured in ‘80s classic Tetris. Made up of 27 smaller cubes, the Soma cube is split into seven subsections of varying shape. In Tetris these subsections slide down the page and it is the player’s goal to slot them together to
Photography: Cheyenne and Temi
welcome to issue#2 aka Delicious Pi We’re going to come right out and say it: maths is beautiful. Numbers are everywhere, and not just in the classroom or in the maths block. The possibilities are endless. You can see numbers in nature, in humans, in everyday life and throughout the design of Thomas Tallis School. Within these few pages of Delicious Pi we are going to take you on a journey to see how maths affects absolutely everything. And who knows, it might even change your view of the world. In this fanzine you can find out how supercool designer Kate Moross used her love of vectors to design clothing for Topshop, to make artwork for Samsung and BAPE or to make her new video for Jessie Ware.
Or... How maths affects our subconscious in manipulating the way we view someone's appearance. Or... the ways in which a drummer, writer and maths geek used mathematics to help him make the funkiest noise possible. Or... the mathematical side to art, like Cubism or Islamic shadow folding. There is so much more in our second Tallis Fanzine. We interviewed Simon Thomas to find out more about designing mathematically inspired sculptures. There’s even maths in literature, as you’ll find when you read our interview with journalist and author Alex Bellos.
The dictionary’s definition of mathematics is the systematic treatment of magnitude, relationships between figures and forms, and relations between quantities expressed symbolically. But is that all there is to it? We think there’s more to life than that and we hope you will too. Hopefully there’s enough in here to open your eyes to the magnificent world around you in all its beauty. There's more delicious pi at www.creativetallis.com
Think about this: the entire world around us is full of cosmic uncertainty and randomness, and the most beautiful thing about maths is surely that it puts that chaotic world into some form of order and logic. As you flick through these pages the mathematical awesomeness of drumming, buildings, Ancient Greek and Islamic art, the human face, photography, architecture and even bubbles will hopefully become clear to you.
In The Fold Delicious Pi present their top tips for shadow folding in cloth. Words: Kim Craig and Erin Callanan
Illustration: Alex Golin
Shadow folding is a type of Islamic art in which you sew the corners of shapes in fabric and pull them together. Islamic art is centered around Allah and the belief that “all you believe him to be, he is not”. Because of this, Allah is represented with geometric patterns. The patterns are similar to the Arabesque style, which also involves repeating geometric designs. The outcome of your work will be to create folds in the fabric that result in beautiful patterns like the one seen here. Although the art may be beautiful, it is almost never perfect, as mistakes in repetitions may be intentionally introduced as a show of humility by artists who believe only God can produce perfection.
There are only 10 types of people in the world: those who understand binary, and those who don't.
Here are some tips to creating the perfect – or not so perfect – piece of shadow folding. Plan out your template first, and make sure all of the angles and lengths of the shapes are exact. When planning your template, use regular, geometric, symmetrical shapes. Make sure you have a large amount of cloth as it gets very small when folded. Mark out your template with something visible like chalk. Use strong, thick thread when sewing to prevent snapping, preferably a cotton linen blend, and for the fabric use a silk or a tight cotton weave. Concentrate - don’t get confused! Never sew all the way through the material, only ever through 2- 3 threads. Leave long end strands after tying each individual shape, to prevent snapping. Iron your cloth to sharpen your folds. Only fold your cloth after sewing all the points together.
IS FOR VECTOR
Words: AJ Kamat
Interview by Ben Linden and Joe Brown
Kate Moross is a graphic designer who pops up in NME lists (well, in their list of Future Innovators), who has designed artwork for Mystery Jets, Simian Mobile Disco and Mark Ronson’s Allido record label, and who has made clothes for Topshop and posters for Cadburys. Oh, and she’s a total vector geek. We caught up with her on Twitter. @creativetallis What was your experience of maths at school like, did you study it after GCSE? @katemoross I was pretty rubbish at maths, but I did Physics A level. I loved the idea of it but was never great with numbers. @creativetallis Your creative process: do you start with geometric shapes or do they work their way in as you go? @katemoross A bit of both I think, I like using them as a foundation when I haven't got any other imagery, but I also use them as fills. @creativetallis How do you use vectors? @katemoross I choose vectors over pixels any day. Nearly all my work is vector now because it can be blown up massive.
@creativetallis How do ratios between size/shape affect your designs? @katemoross It's not something conscious I just do what ever I feel looks good. @creativetallis How important is scale and shape repetition in your work? @katemoross ^^^^^^^^^^^^^^ everything is made from shapes - look up the theory of geons. www.katemoross.com More maths-inspired designers... • Issey Miyake • Elisa Strozyk • Galya Rosenfeld • Lucy Mcrae • Rinus Roelfs Want to find out about maths-inspired designers? Have a look online www.creativetallis.com
Did you know that during your lifetime you will eat about 52,678 slices of bread? Think about what you eat, use and discard in an average lifetime. Now calculate it for every person in England, now every person on Earth. If one person can eat that much bread, then think about how much bread will be consumed for the entire population on earth in their lifetime. Assuming that everybody in their lifetime eats roughly the same amount, then the total is over 358 BILLION slices of bread! There are approximately 301 million people living in the US and if we take the average lifetime of an American to be 78 years old, then we can calculate the average American’s human footprint on many things such as amount of petrol and water used and waste produced. In their average lifetime, EACH American will burn 31,350 gallons of petrol, read 5,054 newspapers (about the equivalent of 43 trees), discard 64 TONNES of trash, and use 1.8 million gallons of water! That’s not all. The average American also eats 12,888 oranges,12,129 burgers, and uses 3,796 nappies in their lifetime. That’s around 6 million calories JUST from eating burgers. By their first birthday the average UK citizen will be responsible for more carbon-dioxide emissions than a person in Tanzania generates in a lifetime. The population is said to grow to over 36 billion by 2300. Just imagine how many resources will be used up by the population if there were 36 billion people to account for. Calculate your ecological footprint at www ecologicalfootprint.com
Photo: Florence Hodnett
TAKING MATHS TO THE NEXT LEVEL
Ben Linden was tasked with using his camera to capture the many geometric shapes you’ll find in nature.
Words: Leilah Forward
When I started at Thomas Tallis I hated maths. I despised times tables and honestly never thought I would want to do anything maths-based. What first got me interested was the range of topics it can apply to and its versatility. I love the fact that I can be looking up at the sky and imagine the idea of an equation for how many clouds there are, and to calculate their speed. Once I had discovered, thanks to artist-mathematicians like Escher, that maths existed in a non-numerical form, I knew it was what I wanted to study. A maths degree is one of the most sought-after degrees nowadays and can open so many doors; even so, women make up a small percentage of the people going into maths at degree level. At university I plan to do a degree in pure maths and perhaps one day even a PhD in maths. The reason I want to study a pure maths degree over a science-based maths degree is because I believe I would be able to apply it more. My teachers’ enthusiasm and passion for maths have influenced my decision; they answer all my questions no matter how stupid or unrelated they may appear.
So there I was with my camera. The first thing I spotted was a pine cone. Pine cones contain a Fibonacci sequence, where two previous numbers in a sequence add together to make the next. In nature there are angles at every opportunity and the tree branch you can see above shows a perfect right angle. I then found a patch of daffodils and noticed that every single flower had the same number of petals in the same shape and all had a circular shape surrounding the pollen so there was another good example of maths occuring naturally. I decided to move from nature to modern structures and I ventured up to Wembley Stadium. The whole engineering project that was undertaken in building this structure has maths written all over it, but I was interested in a more obvious example of maths: the iconic Wembley arch. The arch bears great resemblance to a parabola which is something we use in maths every day. A parabola is a conic section created from an intersection of a cone which, although doesn’t sound amazing, is used to create a range of objects and buildings from bridges to water fountains. Which is pretty amazing, if you think about it.
Photo: Temi and Cheyenne
Algebra. I don't get it either.
16/32 F X S=
Art, Squared Where does art meet maths? In Cubism, says Erin Callanan. As a child I fell in love with the beauty of art, then I went into secondary education and I grew fascinated by mathematics. The two connected when I found out about a whole style of art based on some basic maths and simple geometry. I am talking, of course about Cubism. You may be familiar with names like Pablo Picasso, Georges Braque and Juan Gris who are part of the early 20th century Cubism movement. Artists from this era are famed for their use of contorted geometric shapes, which was a reaction to the modern invention of the camera. Many artists decided that creating pieces of art that reflected reality was pointless as you could now produce more accurate images with new technology. Picasso and Braque pioneered this movement and developed it as a way of creating pieces that were a gateway into their own psyche that would otherwise be impossible to view. Picasso is obviously one of the most famous Cubist artists and you can see in Guernica the unrealistic use of angles, straight lines and bold shapes.
PRECIOUS TIME Self-confessed nerd and “pretty good drummer” Precious John breaks down the maths behind the beats.
SPEED: S=λf I’ve seen drummers, like Buddy Rich, Thomas Lang, Derek Roddy and Seth Davis reach some insane speeds and I think it’s safe to say that I’ve reached some pretty crazy speeds myself! This is one that requires both physical and mental fitness. Mathematically, you could calculate this by using this formula where S=speed, λ= maximum height of the drum sticks for one stroke, and f=frequency. (Hint: the smaller λ is, the higher the speed)
In Cubist art the subject is generally composed of geometric shapes culminating in the amazingly complex forms. Obviously all art has some connection to geometry because it reflects nature and nature is composed of these types of shapes but the Cubism movement is a drastic exaggeration of the shapes found in nature. For instance many artists do this in portraits where the subject of the piece is evidently a person but the detailing is less obvious, like the features of the person’s face are in the wrong place, or are more angular, with sharp sides and corners. Check out paintings like Picasso’s Angelina, Juan Gris’ Still Life With Guitar or Pompidou by Braque. Cubism is not simply art, it is also an abstract view of the world’s most basic maths.
That’s about enough maths for now but to sound and play like me, master this formula and you’ll be a DRUMMETICIAN in no time. I’m going to leave you with one more thought, which is that musical scales are actually just graphs where time = x axis and pitch = y axis. Crazy.
The ability to play the drums is something everyone wants to do, whether they admit it or not. Being a self - confessed nerd and a pretty good drummer, I’ve been able to come up with a few formulae that expose the maths behind drum technique. I know this is kinda nerdy and unusual for a drummer, but I want to give you a taste of the formulae that make me sound so sick on drums with very little practice, so this is my foolproof drum theory and what goes through my head when I have sticks in my hand: F x S = kick-ass syncopations. TIME: Every piece of music has a specific time signature and every drummer should know when to apply strokes with respect to each time signature. For a drummer this means you have to add, subtract, multiply and sometimes divide fractions in split seconds as these time signatures are given as fractions, like 3/4, 6/8, 4/4, 2/4, 9/12, 16/32. This comes in handy when dealing with sheet music. FREQUENCY: f=v/λ This is the number of strokes a drummer makes within one complete bar of music and the way to calculate this is by using the following formula: f=v/λ where f=frequency, v=speed and λ= maximum height of the drum sticks for one stroke.
Illustration: Claire Sambrook.
New York (CNN). At John F. Kennedy International Airport today, a Caucasian male (later discovered to be a high school mathematics teacher) was arrested trying to board a
From Bauhaus To Tallis
The Bauhaus was a college in Dessau, Germany, which started a whole school of art. Who’s to say Tallis won’t do the same? Words: Joe Brown
The Bauhaus was designed during the 1920s by Walter Gropius to support the development of artists and designers while simultaneously breaking down the barriers between the arts and industry. The leading artists of the time were invited to teach the students at the brand new building in Dessau, Germany. Artists such as Kandinsky, Klee, Moholy-Nagy and Itten worked at the school along with architects like Mies van der Rohe.
Soap and Bubbles
They have created specialist spaces for the visual media and performing arts that will enables students to develop their skills to a very high level. The pioneering legacy of the Bauhaus is felt across the globe and we at Tallis want to play our part in encouraging the kind of innovative thinking and design skills that will help young people to shape our future.
You could say that Thomas Tallis has similar ambitions. Our school has been specifically designed by John McAslan and Partners as a specialist arts college to serve as a creative hub for a brand new community in Kidbrooke. Like the Bauhaus, the learning at the school is supported by professional artists and the school is known for its pioneering work on creative learning. The architects were chosen because of their experience creating buildings for the cultural sector, such as The Roundhouse in Camden and the Trinity College of Music in Greenwich.
Tallis students often work with Year 6 students from Kidbrooke Park Primary, so it was no trouble to nip down the road to make some bubbles – and some connections between secondary and primary. Tallis maths teacher Mr Brown, a group of Year 7s and photographer Esther Collins wanted to show that nature follows mathematical rules. Like what? Well, like the fact that bubbles always meet at angles of 120 degrees in the same way honeycomb does. They also constructed models to create interesting bubble shapes, showing maths can be amazing, and that the subject isn’t just about times tables! They created frames to dip in soapy water, pulled them out and created amazing shapes such as bubble pyramids and cubes. While doing this, students were exploring and creating various 3D shapes without realising it. We blew some onto an OHP and created perfect pentagons and hexagons just using bubbles. Then we found that you can create bubbles inside bubbles, and had some fun making really big ones!
Illustration: Gonzales Neto
flight while in possession of a compass, a protractor and a graphical calculator. According to law enforcement officials, he is believed to have ties to the Al-Gebra network.
MEET MR BROWN Makemaths.com is a website for students and teacher created by our well-respected maths teacher Mr Brown. Luis Sanchez and Precious John caught up with him in the darkroom to find out why mental arithmetic is actually mental. There are some very good maths teachers at Tallis. What’s the secret? Showing people there’s more to maths than just adding, dividing and subtracting. I’m very interested in the abstract. Connecting maths to the real world. Making it fun. What is the most important contribution maths has made to society?
It describes the world around us. And its worst contribution to society? Carol Vorderman. What generally drives your passion for maths? The purity and beauty of it. It’s like intelligence condensed. It’s a language of logic.
Whether you believe the world is run by the illuminati or that the Mayans predicted the end of the world, or if you think it’s all rubbish, you can’t deny that everyone loves a good conspiracy. But what were the Mayans actually on about? Words: Sang Nguyen
Did you have any problems as a young student of mathematics? I didn’t like maths. I thought it was boring because our teacher was boring. I started to like it at A Level because it became a bit more difficult, but I really started to love maths when I became a teacher. What area of maths would you say is your weakest. I’m not very good at mental arithmetic. That’s why it’s called mental arithmetic. Because it’s mental. What made you want to create the website in the first place? Just to bring my teaching to a wider audience and teach people a love for maths. I think maths education is boring and needs to be spiced up a bit. What do you think Scrabble would be like without algebra? It’d be the same. I’ve got a little brain teaser. You’ve got two seconds and I’ll say it only once. What’s 5x6x10 ÷ 200. 1500. It’s 3000 ÷ 200. Aw. It’s 1.5, isn’t it
History has a long and rich tradition of apocalyptic predictions, all of which were wrong. Yet some people still think that this time round, it’s the real deal. Why now? Because of ancient Mayan calendars. Mayan calendars not only recorded the days and years, but also longer cycles of about five millennia. So they could easily make calendars that went thousands of years into the future. But, of course, thousands of years in the future from thousands of years ago brings us to current times when the Mayan calendars stop in 2012. New-age thinkers decided that the wise Mayans stopped making calendars because they knew when the world would end. And because new agers are happy – though scientifically illiterate – people, their vision of 2012 was a great spiritual awakening or world reboot or other hippy-consciousnessexpanding nonsense that the Mayans, who spent time pulling strings of thorns through peoples’ tongues, probably didn’t have in mind. To a normal person the thought that a calendar finishing indicates the end of the world, is an odd conclusion. After all, the amount of time in the Universe is infinite and the amount of stone is limited, so, at some point the Mayans had to stop carving calendars. What should have stayed a fringe belief turned into mass hysteria with the 2012 disaster movie that swept the Academy Awards and the numerous Emmy-nominated apocalypse documentaries on The History Channel. NASA became so inundated with questions that they had to take time away from their busy robot-building, frontierpushing, knowledge-expanding, civilization-inspiring schedule to write a webpage explaining that the humansacrificing, stone-age Mayans, who had neither wheels to pull carts nor glass to make telescopes, didn’t know more about science at the dawn of history than real scientists do today.
He will be charged with carrying weapons of math instruction.
But the parade of crazy marched on anyway making wilder and wilder predictions for Earth including a Geomagnetic Reversal which unfolds on a geological timescale, not a single day; a collision with mysterious Planet X which no astronomer has found; and a galactic synchronization beam, whatever the hell that is. A sane person, at this point, would wonder how the Mayans were able to predict astro-physical anomalies thousands of years in advance and millions of miles away yet didn’t foresee the Spanish coming across the Atlantic. And that’s because the Mayans never predicted apocalypse. The only people to claim the Mayans knew about the end of the world were distinctly not Mayans.
DYING NUMBERS Words: Sianon Foster A hush falls over the crowd, as the balding, middle-aged man pulls the last number out of the hat. The paper makes a deafening crackle in the ghostly silent room, and as his shaking hands unfold it, a sharp intake of breath adds to the symphony. The sunlight streams through the crack in the curtains, and I watch as little pieces of fluff swirl about in the early morning sun. I stay like that, watching them for quite a while and then finally stretch and sit up. Swinging my legs off the bed, I look over to my right and see that Trig’s mattress is empty. My arm tingles and I instinctively look at the numbers inscribed on it. My identity. I sigh and look around me; dirty pieces of clothes lie in piles on the floor, and stacks of papers and boxes compete with my height. I’ve been in this motel for five weeks, in a desert near New York, between an old theatre and piles and piles of rubble. It might not look like much, but to me its home. Home sweet home. Until I have to move on anyway. I’ve been on the run since I turned 15; moving from motels to caves to underground compartments, barely big enough to turn over in, but this is by far the best. I see Trig sitting with some newcomers over at a table in the corner of the dimly lit kitchen. His dirt stained hands hold a mouldy piece of bread and he absent-mindedly
nibbles at it, whilst staring transfixed on the dark man and woman before him. They seem to be telling a story of some sort, but I don’t interrupt, I’m too busy looking for leftovers. No luck. After what seems like an age I settle for a half-eaten granola bar, that looks like it seen better days. I cram it in my mouth as if someone is about to snatch it from me and walk over to where Trig and the newcomers are sitting. As I pull up beside him I notice that he has once more tried to cut the numbers out of his arm. He sees me staring, pulls down his sleeve, and smiling wanly he introduces me to his company. The dark couple are from what’s left of San Francisco and are running from The Augments, just like me. The man says that his number was called up months ago, and he’s been on the run since then. They say that the war isn’t over. They say that the war will destroy Earth. A broadcast on the radio stops the conversation. Any mutterings cease and everyone in the small room stares at it. A list of numbers is read out. They are the numbers of those being called up for the war. Mine is the third. I look down at my arm.
Illustration: Alex Golin
Twist And Solve Callum Hales-Jepp is a Rubik’s cube master. Find out why he loves that multi-coloured square, and how he does it blindfold. “It’s not a toy, it’s a performance puzzle,” he says. The Rubik's cube is a wonderful creation which involves lots of maths, colours and frustration. It was created by Professor Erno Rubik from an idea he got during a lecture in architecture in 1974 and it went massive in 1980. Professor Rubik saw that there were many possibilities for the cube; in fact there were 43,252,003,274,489,856,000 possible combinations. I got into cubing because I had always wanted to know how to do it. I taught myself how to solve it and gradually got better. There are cubing competitions all around the world, which makes it such a great thing to get in to. The thing that I like most is the competitive nature of cubing by trying to get the fastest time. The world record for the cube is 5.66 seconds whereas my record is 20.27 seconds. What is unique about the Rubik's cube is that most of it can be worked out using algebra. Personally I use the Fridrich method which uses 100 algorithms (series of moves) which is the fastest method available. The cube in my perspective is not a toy, it's a performance puzzle which I take seriously. There is more than just solving the standard Rubik's cube. You can solve it blindfolded or with one hand. So why don't you start now?
Decimals. What's the point?
This is the net of a Rubik’s cube which is just three twists away from completion. Can you work out how to complete the net?
Photography: Billy Rowlinson
The Cool Corner Who knew triangles could help prevent buildings from collapsing? Words: Joe Brown
On a recent visit to the Design Museum I came across a product that saves lives: a truly outstanding but simplistic design for an earthquake table. I was shocked by the fact that over 300 million pupils face danger simply because schools are unable to provide adequate protection from earthquakes. The product, designed by Arthur Brutter and Ido Bruno to solve this problem, uses lightweight materials (two children can easily lift it) with built-in crumple zones and a series of triangles. These three components can withstand a tonne dropped it and hold strong. How is this possible? Through design and the magic of triangles. Throughout history triangles have been recognised as the strongest shape, from the roof of the Parthenon to the San Francisco suspension bridge, they literally hold up and support the world we have created. I wanted to find out for myself what the triangle can really do. We can crumple and tear paper, but with the right folds it can be very strong. I created a flexible but strong backbone like structure and was shocked by the result. It really highlighted how nature and evolution has created durable and robust shapes. Art and science should always look to nature for solutions and inspiration. Photography: Year 12 photography students
ALEX’S ADVENTURES IN NUMBERLAND
Guardian and ended up in South America, writing about football. When I came back from Brazil, I had kinda forgotten about maths. I thought why don’t I go back and try and use the skills I’ve learnt to write about maths?
feeling of ‘wow’, an almost emotional reaction to seeing the proof. The way to describe the effortless simplicity and efficiency of being reduced to the most simple thing from nothing, there is a beauty to that.
You said maths was your favourite subject at school, how does modern day teaching of the subject compare to the ‘70s?
Your book Alex’s Adventures in Numberland. Does it have any connection to the maths found in Lewis Carroll's Alice in Wonderland?
At primary school they brought in this new thing called set theory, which turned out to be completely crazy and rubbish so they stopped it. The maths I did at O Level [GCSE] has been moved to A Level or erased completely, like imaginary numbers which is really fun and exciting (e.g square root of -1) which isn’t even taught at A level. Now you need to do further maths or go to university. Some methods are improved because it has lost the learning by rote approach.
No. The book was originally called the Book of Numbers Took Its Own Path. Then someone said ‘adventures in numberland’ because it was a joke on Alice, which is known to be very funny and a very maths-y book.
You mentioned you like pi, is there anything about maths that particularly fascinates you?
Words: Kim Craig and Erin Callanan. Illustration: Alex Golin
Some may know him as a sports writer for the Guardian newspaper, but Alex Bellos is more than a pitch lurker. He recently came to our attention with his book Alex’s Adventures in Numberland where he breaks down historical mathematical theories and stories by using engaging narrative and real life examples. What encouraged you to make the transition from writing about football to writing about maths? Well, at university I did maths and philosophy. At school maths was my best subject, but I was always quite interested in writing for newspapers. I wrote for the
I’m much more interested in philosophical side of maths like the big questions. If you said calculate the height of a mountain I wouldn’t be interested, because there’s a method and you can do it. I’m much more interested in infinity; can you get different sizes of infinity? Or Zeno's paradox. I love paradoxes. I like things that you’re not sure how it’s worked out and maybe you can’t resolve it. It makes you think about the type of world we live in. You like to think the world is about logic but some things in maths are illogical, I like that. I like the pure side of maths. Tell us why you think maths is beautiful? I think it was Bertrand Russell that compared it to the ‘cold beauty of sculpture’. It’s not something that is aesthetic like a painting or a piece of music, it’s something that is clean and efficient and clever. For my book I did a number of the visual proofs for Pythagoras’ theorem and you have this
What’s your next book about? It’s going to have bits of trigonometry and I’m going to try and explain calculus, as calculus is the maths of change. I’m also going to explain e, it appears a lot more than pi, and is probably the most important mathematical concept.
Want to know what a maths author reads? Here are three numberish books Alex recommends. A graphic novel called Logicomix by Apostolos Doxiadis and Christos H. Papadimitriou Simon Singh’s The Code Book Anything by Martin Gardner
SIMON THOMAS Words: Tom Warner
Simon Thomas is a sculptor who bridges art and science How long have you been making sculptures inspired by maths? I was playing with 3D before I knew what I was doing, but formally I started making sculptures in 1978. My Dad was a very good woodworker and I suppose I wanted to be a bit like him. Do you think that the importance of young people working with their hands has been lost?
Photography: Florence Hodnett
I think the art world generally is the same as the rest of the world. There is this chasm that has opened up between intellect and dexterity. The greatest person in my mind is the person who can marry the two: someone who has a intellectual and a dextrous dimension.
Projecting the fourth dimension
What inspires your work? I’ve always been fascinated by nature, especially things like evolution, how it works and the forms it takes. I’m very interested in efficiency, which is why geometry has always fascinated me.
Dimensions! They’re one of the most simple ways to understand how our world is built up, but do we really know as much as we think? Words: Caleb Forward and Rhianna McGill
Did you enjoy maths at school? I was very average at school. I didn’t see my relation to it clearly, so I didn’t see the worth of it. It seemed to be an abstract kind of pursuit, that didn’t have an anchor in the real world. Which is obviously true, I mean, maths is all spiritual or intellectual. So I saw it as something foreign, that I wasn’t used to.
We embarked on a mission one lesson to create a three dimensional (3D) representation of a four dimensional (4D) shape. When you think of a fourth dimensional shape it’s generally a bit of mystery. People assume that they won’t be able to begin to perceive one as we’ve never seen the fourth dimension. But is this really true? Can we not at least know what a projection of one would look like in the third dimension? Before we reveal how we made our 4D dodecahedron here’s a refresher on dimensions: 0-D Dot, 1-D Line, 2-D Square, 3-D Cube
A bit like a foreign language? I did what I had to get an O-level in maths and I was so relieved, thinking I would never have to do maths again. And being a sculptor I re-entered maths through a pleasant route. Your own interest sucks you in. I found that, to learn something you’ve really got to like it. But I’ve got massive holes in my understanding of mathematics, I only know tiny little bits, but I know them quite well. When people struggle with maths they sometimes go inside their head. What about you? I go inside my head quite often. When Einstein was doing his theory of relativity, he didn’t have a proper library to go to. He didn’t have access to other physicists. He was an intellectual, who was able to ponder something. In one of his papers, he didn’t have any references at all. He thought it all up. And to me that’s just pure creativity. Beautiful, but unbelievable. Were you a bit of a daydreamer at school? I was. I don’t think you can waste time intellectually by daydreaming because it all goes in. It’s like having a jar of muddy water and shaking it up. Eventually it will all settle down.
As you can see, a third dimensional (3D) representation of a cube can be drawn in two dimensions as a square connected to another square by lines which with the sides of the squares form contorted squares. A three dimensional representation of a fourth dimensional hypercube can be made by joining two cubes by lines connecting the vertices of one to the equivalent vertex. This creates contorted cubes between the two original cubes. Now we can see it on paper how do we go about making it in real life? The construction of the 4D dodecahedron began with a 3D dodecahedron (12 regular pentagons connected together). We then created irregular shapes, constructed with 12 irregular pentagons. This is because it is a shadow of a 4D shape which will include warped versions of the original shape, just as a 2D representation of a cube contains contorted squares as rhombuses. Layers of irregular dodecahedrons were made and attached to the original to give an impression of what a hyperdodecahedron would look like. We did it, basically.
What inspires your drawings?
SKETCHUP 3D Tallis student Sammy Harpin is a young illustrator. He’s also a big fan of Google SketchUp. Kar-Ho Cheung finds out why Year 11 student Sammy Harpin is on the cusp of completing his GCSEs and aspires to work in the creative industries. When he’s not studying he’s familiarising himself with Google SketchUp; an open-source programme that allows anyone to create 3D and 2D models. How long have you been drawing on Google SketchUp ? About two years it all started when my brother downloaded the software. I played around on it drawing small simple shapes but as time passed these shapes built up and became complex structures.
I’m not too sure. I look at images on the Internet, interesting buildings in games and films, whatever catches my attention. I just observe things and see what I can create. I gain inspiration from architect Norman Foster.
You can find out more about Sammy’s work at: flickr.com/ photos/sammyharpin Google SketchUp is a free drawing programme that you can use online: sketchup.google.com
When you’re designing something do you think about the mathematics behind your design? The good thing about Google SketchUp is that you don’t need to worry about the maths, there is no need for me to think about it as the programme does it for me. Do you think there’s a link between maths and art ? Yes, there is a big link between the two as a lot of artwork has mathematical principles which allow them to work. What are your hopes and aspirations for the future? I would like to be an illustrator. I would like to use some of the architectural work I have done to make new different designs and to add my own artistic flair to existing designs and illustrations.
contributors AJ Kamat
BEAUTY IS GOLDEN
Alex Golin Ben Linden Billy Rowlinson Caleb Forward Callum Hales-Jepp Cheyenne Joseph Claire Sambrook Emily Mahon Erin Callanan Esther Collins Florence Hodnett Frankie Mayo Gonzales Neto Joe Brown Kar-Ho Cheung Kim Craig Leila Forward Luis Sanchez Precious John Reuben Thomas Pain Rhianna McGill Sianon Foster Temi Omolekulo Tom Warner
Kim Craig, Erin Callanan and Rhianna McGill tell all about Fibonacci, why David Cameron is weirdly symmetrical and (maths joke alert!) delicious… phi. Back in 2001 an orthodontist by the name of R.J Edler wrote a paper claiming that that the more symmetrical your face was, the healthier you were. He was talking about the golden ratio, when two consecutive numbers from the Fibonacci sequence are divided by each other and equals something close to 1:1.618. This is found everywhere in nature, and especially in people’s faces. The spirals formed through the numbers being represented as squares are found everywhere in nature, in shells, flowers and even the human ear. So what exactly is the Fibonacci sequence? It goes 1 1 2 3 5 8 13, with each number being formed by adding together the two previous numbers. If you divide a Fibonacci number by the previous one you get a number close to the Golden Ratio or phi, and the larger the numbers the closer to phi (ϕ) you get. For example, 89 divided by 55 equals 1.618181818.
Measure, in centimetres, the distance between: A The top of your head to your chin B The top of your head to your pupil C Your pupil to the tip of your nose D Your pupil to the centre of your lips E The width of your nose F The outside distance between your eyes
The golden ratio is also found in human faces. The more golden ratio that can be found in your face the nearer a ‘perfect’ example of humanity you are. Another way of judging beauty is by how symmetrical someones face is. No-one has a perfectly symmetrical body, although when we tried this out on David Cameron we found he was weirdly symmetrical!
G Width of your head, from the temple
To test if you’re the person we should send into space to represent Earthlings then do as follows...
L The tip of your nose to your lips
H Your hairline to your pupil I
The tip of your nose to your chin
The centre of your lips to your chin
K The length of your lips
Then divide A by G, by D, I by J, I by C, E by L, F by H and K by E, if these are around 1.6 then you are perfect. But does that necessarily imply beauty?
Numbers are everywhere. But not everyone knows they are beautiful. Students at Thomas Tallis, which is a specialist arts college and school of creativity, definitely understand why numbers matter. Maths fans, young journalists, photographers and designers from Year 10 to Year 13 got together to create this publication with the support of creative professionals. Like many Tallis projects the aim was to provide a creative experience that has practical outcomes. As well as spreading maths love, students who took part can use Delicious Pi when they apply for university or apprenticeships or jobs. A special thank you to the whole maths department and to Mr Brown, Mr Nicholls and Ms Barton who helped with the making of this fanzine. ~ Design and Mentoring Darryl Daley Editorial and Mentoring Hayley Joyes Editor Emma Warren
The SOURCE OF TALLIS Photos: Billy Rowlinson, Esther Collins and Emma Frarrant
Thomas Tallis School is situated on the curve of Kidbrooke Park Road. When the architects were designing the plan of the new building they decided to imagine that this arc was part of a circle with an imaginary central point. The radial lines emanating from this point define the edges of the wedge-like shape of the new school structures. We decided to send Billy, Esther and Emma to see if they could find the centre of the circle. Their journey to the source and back is recorded in a series of photographs. X marks the spot.