the mathrigals NAVA, MONDIA, AGUADO, SOURIBIO, GABRIEL GROUP 1
on nava r b le
us sourib k r i ma
o
mond i s y ia je guado a m ba
is gabrie r h l c
Table of contents ALGEBRA
Father of Algebra Cartesian Plane Ways to Solve Quadratic Functions Infographics Snake&Ladders Song Lyrics QR for Videos
1 1 2 3 5-6 7 8
TRIGONOMETRY Father of Trigonometry History of Trigonometry Pythagorean Theorem Angles in Standard Position Infographic Greek Letters Triangle Artworks
9 9 9 10 11-12 13-14 15
PLANE GEOMETRY Father of Plane Geometry History Of Plane Geometry Proving Statements Ways to Name Shapes Crossword puzzle
17 17 18 19-20 21-22
OTHERS Guess the Character Memes Bibliography
25-28 29-30 31
1
Algebra DO YOU UNDERSTAND? (7ft fra-) Father of Algebra Muhammad ibn Musa al-Khwarizmi is the father of Algebra. He lived in Baghdad between 780 to 850 CE (or AD). His work offered practical solutions for land distribution, inheritance, and distributing salaries. He wrote the book “Hisab Al-Jabr” and that’s how algebra got its name.
SONG
(-8 ,-8 )
( - 4 ,- 9
)
CARTESIAN PLANE
We Don't Talk about Bruno
Ways to Solve Quadratic Functions 1. 2. 3. 4. 5.
(-11,5)
Square Root Method Factoring Completing the Square Quadratic Formula Graphing
ional imens d o w at ne ate pla n i d r o co he d by t forme e n of th o i t c e . inters y-axis d n a s i x-ax
(-5,5)
2 (-9,10 )
SQUARE ROOT Factoring METHOD f(x) = x²-25 x²-25=0 x²=25 √x²=√25 x=±25
5 (ac) 5
Completing the square
(5,9)
f(x) = x²+6x-7 (6/2)² = 9 x²+6x-7 = 0 x²+6x + (__) = 7 x²+6x + 9 = 7+9 √(x+3)² = √16 x + 3 = ±4 x = -3±4 -> x₁ = -7, x₂ = 1
1 6 (b)
f(x) = x²+6x+5 A = 1, B = 6, C = 5 (x+5)(x+1)=0 x₁ = -5 x₂ = -1
Quadratic Formula f(x) = x²+6x-7 A = 1, B = 6, C =- 7 x²+6x-7 = 0 -6±√-6² - 4(1)(-7) /2(1) -6±√36 + 28 2 -6±√64 2 -6±8/2 -> (-14/2, 2/2) x₁ = -7, x₂ = 1
GRAPHING
3
4
5
2 1
-5
-4
-3
-2
-1 -1 -2
The Quadrant of... (-5,1)
(4,2)
(3,0)
6
2 1
1
2
3
4
-1 -2
(-5,-1)
(-4,2)
(1,2)
5
7 Quadratic Formula Song [Verse 1] If you try to solve a quadratic equation I promise you: It's possible without any frustration If you take everything, move it to one side Sort by x squared, x and the rest. Alright Take the coefficients, name them a, b and c And if you know the right formula, you will see That you get the solution in the very next step Just sing this song in your head: [Chorus] Negative b plus or minus the square root of B squared minus 4ac over 2a Negative b plus or minus the square root of B squared minus 4ac over 2a [Verse 2] Okay. Let's start with our equation and our job is going to be Solving this now for x, so let's take minus c Multiply by 4a and if you now add b squared It all looks way to complicated, but don't be scared Just take a close look to the left side and you'll see: There's a binomial formula with 2ax and b So altogether this is the square of 2ax+b And now we have only one x, so the next step will be To get rid of the square and if the right side is not negative The square root must be one solution, but there's an alternative 'cause minus the square root yields the same if you square it So we write "plus minus" and now we are at the point, where it Only takes two more steps to solve it for x And if you look to the left side, you know what will be next: Subtraction of b and division by 2a is giving us our formula for x. Okay. And it's [Chorus] Negative b plus or minus the square root of B squared minus 4ac over 2a Negative b plus or minus the square root of B squared minus 4ac over 2a Negative b plus or minus the square root of B squared minus 4ac over 2a Negative b plus or minus the square root of B squared minus 4ac over 2a
8
Rene Descartes We do not describe the world we see, we see the world we can describe
Mathrigals as teachers
Mr. Nava
Mr. Mondia
Mr. Gabriel
Mr. Souribio
Mr. Aguado
9
Trigonometry HE TOLD ME THAT... Father of trigonometry Hipparchus was a Greek mathematician who compiled an early example of trigonometric tables and gave methods for solving spherical triangles. Hipparchus contributed to trigonometry early on, developing a table of chords, an early form of a trigonometric table.
PYTHAGOREAN THEOREM developed by Pythagoras himself.
c =a +b 2
2
2
history of trigonometry The Greek words trigonon ("triangle") and metron ("to measure") are used to form the word trigonometry. It is fouces on determining the numerical values of missing portions of a triangle If you know the lengths of two sides of a triangle and the measure of the contained angle, you can calculate the third side and the two remaining angles.
SONG La Familia Madrigal
10 Angles in standard position An angle is in standard position if its vertex is located at the origin and one ray is on the positive x-axis. The ray on the xaxis is called the initial side and the other ray is called the terminal side.
ter min al sid e
Initial side
If measured in a counterclockwise direction the measurement is positive. If measured in a clockwise direction the measurement is negative.
Fun Fact! Engineers use Trigonometry to figure out the angles of the sound waves and how to design rooms. - Leonardo Da Vinci
120°
If two angles in standard position have the same terminal side, they are called coterminal angles.
-240°
11
12
13
Greek letters
14
Greek letters
15 triangle artworks
16
Hipparchus "Never deceive a friend."
17
Plane Geometry We don't talk about Euler... Father of PLANE GEOMETRY Euclid is considered the father of Geometry. HIs contributions to Geometry can be found in his book "The Elements". It's a 13 part book that explains everything there is to know about Geometry. There are many renowned geometers but Euclid is known to be the one who has contributed the most.
SONG:
Dos Oruguitas
history of PLANE GEOMETRY Plane Geometry is a topic that has existed for a long time. The earliest examples are with the Ancient Egyptians who have devised a mathematical equation in order to equally divide land, constructing buildings, and different techniques that still exist today. The Greeks were able to gather and extend this knowledge to form the less practical but more mind boggling version of Geometry we know today.
Dos oruguitas enamoradas Pasan sus noches y madrugadas Llenas de hambre
The basic elements of plane geometry are lines, points, and planes. Points are dots, lines are just long straight marks without curves, and lines may form a plane once connected.
18
Modern Postulates Since proving is an important part of geometry, this document will share the postulates you might need.
Did you know? Everything is made out of shapes. Try looking outside your window and look for different variations of squares and other 3 dimensional shapes.
Example: Basic Postulates (eUClid's books) Given 2 points there's one straight line that joins them A straight line can be prolonged indefinitely A circle can be constructed when a point for its center and a distance for its radius are given. All right angles are equal.
HOW TO PROVE:
≅ NO, and ∠M ≅∠O Prove: △MPL ≅ △NPO Given: LM
Statements
≅ NO ∠ ≅∠O ∠ ≅∠OPN △ ≅ △NPO LM M MPL MPL
Reasons Given Given VAT AAS
19
NAMING SHAPES Introduction to naming shapes Did you know different shapes have different names? For example, a shape with 546 sides is called a hectapentatetracontakaihexagon. Shapes are an important part of geometry and we're gonna teach you how to name them. You can name shapes using the chart below. Substitute each number to each space in the graph and add the words together to get the final result. That's basically it! Now you can name every shape ever! (below 999)
Number
Hundredths
Tens
Ones
1
Hecta
deca
Henagon
2
Dihecta
Icosi
Digon
3
Trihecta
Triaconta
Trigon
4
Tetrahecta
Tetraconta
Tetragon
5
Pentahecta
Pentaconta
Pentagon
6
Hexahecta
Hexaconta
Hexagon
7
Heptahecta
Heptaconta
Heptagom
8
Octahecta
Octaconta
Octagon
9
Enneahecta
Enneaconta
Nonagon
10
N/A
N/A
Decagon
20
TRY IT! Name the following polygons (use the table as a guide for its place values)
643
893
478
235
79
347
hectahexa
tetracontakai
trigon
21
8
22 8
23
ANSWER KEY TRY IT!
CROSSWORD
643
hectahe xa
tetraco ntakai
trigon
893
octahec ta
enneac ontakai
trigon
478
tetrahe cta
heptac ontakai
octago n
235
dihecta
tetraco ntakai
pentag on
79
N/A
heptac ontakai
nonago n
347
trihecta
tetraco ntakai
heptag on
1. Pentagon 2. Pythagoras 3. Triangle 4. Archimedes 5. Pascal 6. Thales 7. Nonagon 8. Euclid 9. Circle 10. Descartes 11. Plato
24
Eukleides "Euclid" "There is no royal road to geometry."
25
GUESS THE CHARACTER! A-C D-F G-I J-L M-O P-R S-U V-Z
0 ±1 ±2 ±3 ±4 ±5 ±6 ±7
26
GUESS THE CHARACTER!
f(x) = 0 f(x) = 0 f(x) = x^2-16 find the roots find the roots find the roots
f(x) = x^2-4 find the roots
f(x) = x^2-9 find the roots
27
GUESS THE CHARACTER!
f(x) = x^2-9 f(x) = x^2-36 f(x) = x^2-4 f(x) = x^2-36 f(x) = x^2-16 find the roots find the roots find the roots find the roots find the roots
28
GUESS THE CHARACTER!
f(x) = 0 f(x) = 0 f(x) = x^2-16 f(x) = x^2-4 f(x) = x^2-9 f(x) = x^2-16 find the roots find the roots find the roots find the roots find the roots find the roots
Memes
Reference page Artmann, B. (2020). Euclidean geometry. Encyclopædia Britannica. Retrieved March 2, 2022, from https://www.britannica.com/science/Euclidean-geometry Al Jazeera. (2015). Al-Khwarizmi: The father of Algebra. Science and Technology | Al Jazeera. Retrieved March 2, 2022, from https://www.aljazeera.com/program/science-in-a-goldenage/2015/10/20/al-khwarizmi-the-father-of-algebra Barnard, R. (2020). Trigonometry. Encyclopædia Britannica. Retrieved March 2, 2022, from https://www.britannica.com/science/trigonometry Bourne, M. (2017). Al-Khwarizmi, the father of algebra. intmathcom RSS. Retrieved March 2, 2022, from https://www.intmath.com/basic-algebra/al-khwarizmi-father-algebra.php DorFuchs. (2016). Quadratic Formula Song. YouTube. Retrieved March 2, 2022, from https://www.youtube.com/watch?v=J51ncHP_BrY Heilbron, J. L. (2020). Geometry. Encyclopædia Britannica. Retrieved March 2, 2022, from https://www.britannica.com/science/geometry Introduction to plane geometry. Introduction to plane geometry - Math Open Reference. (2011). Retrieved March 2, 2022, from https://www.mathopenref.com/planegeometry.html Kiger, P. (2021). What are imaginary numbers? HowStuffWorks Science. Retrieved March 2, 2022, from https://science.howstuffworks.com/math-concepts/imaginary-numbers.htm Lowell Milken Center. (n.d.). Meet the Hero: Muhammad ibn Musa Al-Khwarizmi. Retrieved March 2, 2022, from https://www.lowellmilkencenter.org/programs/projects/view/muhammad-ibn-musa-alkhwarizmi/hero Morris, S. (n.d.). The pythagorean theorem. Retrieved March 2, 2022, from http://jwilson.coe.uga.edu/emt669/student.folders/morris.stephanie/emt.669/essay.1/pythagorean.ht ml Science Focus. (2020). A brief history to imaginary numbers. BBC Science Focus Magazine. Retrieved March 2, 2022, from https://www.sciencefocus.com/science/a-brief-introduction-to-imaginarynumbers/ Taisbak, C. (2021). Euclid. Encyclopædia Britannica. Retrieved March 2, 2022, from https://www.britannica.com/biography/Euclid-Greek-mathematician TRIGONOMETRY IS FUN ! (n.d.). Fun facts! Trigonometry is fun ! Retrieved March 2, 2022, from https://trigonometryisfunyay.weebly.com/fun-facts.html
INSPIRED BY: sir regie lighting the Encanto candle
sir luigi blooming flowers sir gary spying on Mirabel