MARCH 2022

ISSUE 8

MATH POSSE

YOUR MATHEMATICS MAGAZINE

FIND YOUR BEAUTY

THE BEAUTY OF THE NATURAL WORLD WITH MATHEMATICS

EXISTENCE OF MATH EVERYWHERE WE LOOK

SEEING MATHEMATICS THE MATH POSSE WAY

How does the nature relate to math?

Where exactly can we see math around us?

What is the best way to look at math from just numbers?

CONTACT US F.M. Box 112, 35813 Bonifacio Rd. Manila 9956543862 99164873266 posse@math&nature.com www.themathposse.com

EDITORIAL ALLERIE FARIOLA Editor

ABOUT MATH POSSE We'd love to see you inspired.

We would like to welcome you all to our Math Posse magazine. These shall serve as a motivation dedicated to showing the beauty of Mathematics through nature. The word posse is defined by the Meriam-Webster dictionary as a large group often with a common interest. Both of the authors collaborate and share their interest in Math that has been written exclusively for the magazine.

Anyway, we hope you enjoy this one. ALLERIE FARIOLA & KATE MANZANO Editors

Editor

CONTRIBUTORS Unsplash.com Merriam-Webster Dictionary

SUBSCRIPTIONS SUBSCRIBE ONLINE www.themathposse.com/ subscribe HOTLINE +20 (54) 582 29 49

MATH POSSE | PAGE 1

The purpose of this is to give individuals a new perspective on mathematics by relating it to nature. We wanted something to make people understand and appreciate math, and one of the most effective ways we see is to link it with nature as we, on a side note, are a significant part of it. The reason why this is important was quite simple: It’s because it helps us understand math and the world.

KATE MANZANO

CONTENTS pg. 01

pg. 09

ABOUT MATH POSSE

EVERYTHING IS ORGANIZED WITH SEQUENCE

pg. 03

pg. 10

TRIVIA OF THE DAY

PRODUCING THE BAD DIFFICULT AND THE GOOD EASY

pg. 04

pg. 11

THE BEAUTY OF MATH IN NATURE A WAY OF SEEING INFINITY

pg. 05

pg. 12

WHERE THERE IS BEAUTY, THERE IS GEOMETRY

WORDS FROM THE EDITORS

pg. 07

pg. 14

WHAT WE SEE AT A GLANCE

SOURCES

MATH POSSE | PAGE 2

"The Ancient Greeks believed that if you studied numbers, you had to be a person who did not need to work because you would probably be a person who was interested in strange & wonderful things. Who studies numbers today?"

MATH POSSE | PAGE 3

DID YOU KNOW?

THE BEAUTY OF MATHEMATICS IN NATURE

MATH POSSE ALLERIE KAYE A. FARIOLA KATE WINSLET MANZANO

Math is literally everywhere our eyes lie. Most people, if not all, grew from their educational years learning that mathematics shall be and will always be confined in the spaces between books and will be alone spoken in the corners of the classrooms. You shall be stood corrected as this edition is about to teach you the beauty to be found within the natural world. Have a quick look around. You may not see lines, numbers, figures, symbols, shapes, and the like; however, I can assure you that what is beside, in front, and whatever & wherever your eyes are laid right now, they speak of math and they are math themselves. It shall be debunked the idea that the word mathematics simply implies the use of the figures we learned from our kindergarten days to today. After all, the natural world, together with math, is endowed with beauty.

Nonetheless, this new release of the Math Posse aims to flourish your understanding of the field of mathematics. By the end of your reading, it is in our greater hopes that readers would come to a fascinating realization that understanding nature is understanding mathematics.

MATH POSSE | PAGE 4

As we go on with our lives, we seldom see mathematics outside our classes as it is almost impossible to hear the word linked to the environment, the natural world.

R E P R E S E N T A T I O N S

M A T H

I N

O F

GEOMETRY

N A T U R E

WHERE THERE IS BEAUTY, THERE IS GEOMETRY One way to represent mathematics broadly in nature is by Geometry. From its etymology, geometry in Greek word means the measure of the earth. Geometry is seen in every aspect of the world. Through geometrical shapes, we can see the beauty of nature in its different forms, and the same with math, we can see its beauty by nature. We get to identify and know everything in this world from its shapes while looking at each corner.

M A T H P O SRS E I |S EP A| GP EA G 5E 4

When we were kids, we learned the fundamentals of shape, area, and volume. We also use different tools such as protractors and various rulers when we have an activity about measuring something around us. Geometry lets us know how these shapes fit each other, which helps us set everything in order and understand the beauty in its own shape. Basically, geometry is living with us, as we get to use all of our senses, everyday we experience geometry. We have encountered the different kinds of forms and their differences in math. But as we go deeper into nature, we learn that they are inextricably linked.

R E P R E S E N T A T I O N S

M A T H

I N

O F

N A T U R E

GEOMETRICAL SHAPES

MAYON VOLCANO CONE SHAPE Mayon volcano is the Philippines' proudest and most famous volcano. It is known for its perfectly symmetrical cone shape with a height of 8,077 feet/2930 meters.

FINGAL'S CAVE HEXAGON SHAPE An astonishing cave-in Scotland with hexagonal column shapes formed as the solidified lava flows cools off on its upper and lower surface.

FACIAL BEAUTY

In mathematics, physical beauty is measured its divine proportion through a geometric representation such as its points, distance, and symmetry.

MATH POSSE | PAGE 6

THE IDEAL SHAPES OF BEAUTY IN MATH

R E P R E S E N T A T I O N S

M A T H

I N

O F

N A T U R E

On a daily basis, people define symmetry as a sense of sharing harmonious relationships

WHAT WE SEE AT A GLANCE

between

things,

shape,

and

space

while

grounded on balance and proportion. This correspondence

between

surface

level,

sharing

invariance

pertains

things,

to

with

the

the

on

a

quality

of

lateral

part,

generally referred to as reflection, rotation, translation, and scaling. In the context of biology,

symmetry,

classification

SYMMETRY

types.

as

well,

Symmetry

has

its

showcases

unusual yet great efficiency in attempts to decrypt and comprehend the cosmos. The

Out of all the representational to be found

in

this

magazine,

next

to

geometrical shapes (pg. 05), the word symmetry

is

what

we

hear

often

the

bilateral,

spherical,

and

radial

types

of

symmetry encompass the world due to its existence believed

even by

in

the

the

universe,

Ancient

as

Greeks.

widely

On

the

most. However, little do our minds know

other hand, put in mind that symmetry can

and realize that it does not simply exist

be

in our nature, but plays a role, and a

alone, but as well as the internal structures

significant one at that.

of organisms.

sighted

not

just

in

external

features

MATH POSSE | PAGE 7

R E P R E S E N T A T I O N S

M A T H

I N

O F

N A T U R E

SYMMETRY IN NATURE

01

03

02

DOES IT ACTUALLY EXIST?

01

organism concerning to a central axis or point. A single minority in the abovestated seen, then an asymmetry is implied.

Bilateral Symmetry

Symmetry elementally imparts order, both internally

A butterfly exhibits a strong

and externally. Thus, people are known and

resemblance in its anatomical parts

observed to be attracted more to symmetry as it

on the sides of a median axis.

introduces its own aesthetic which is generally viewed as pleasing to the eyes. The approximation,

Spherical Symmetry

exquisiteness, and beauty is no coincidence– it is what we see at a glance.

With its body shaped like that of a sphere, the volvox green algae, under a light microscope, shows symmetry concerning a line or point.

03

strict balance and proportion between parts of an

TYPES OF SYMMETRY IN BIOLOGY

01 02 03

Radial Symmetry There is a fascinating fact within the formation of snowflakes in clouds resulting in its six-fold infinite symmetry.

Bilateral Symmetry Spherical Symmetry Radial Symmetry

TYPES OF SYMMETRY IN DESIGN

04 05 06 07

Reflection Rotation Translation Scaling

MATH POSSE | PAGE 8

02

Biological symmetry, in its definition, pertains to the

R E P R E S E N T A T I O N S

M A T H

I N

O F

N A T U R E

EVERYTHING IS ORGANIZED WITH SEQUENCE Fibonacci Sequence



Have you ever wondered how things seem to be pleasing in the eye? It is because of the Fibonacci sequence that everything we see is organized. In mathematics, the Fibonacci sequence is an orderly pattern of numbers. Before we find the answer in every mathematical equation, we solve it by writing an organized number sequence. They said that this numerical sequence is in, fact, nature’s secret code, which helps us to understand the process of how everything works. Through the Fibonacci sequence, we can understand nature through its natural process and how they are connected.

RABBITS Several observations found a numerical sequence in the reproduction of paired rabbits. The paired rabbits have always reproduced paired offspring of both opposite sexes. The paired rabbits reproduce another pair, as this continues and increases every month pass by.

PEACOCK'S FEATHERS

OAK TREE Its branches, trunk, and leaves have shown a trace of the Fibonacci sequence and interpreted in fractions. A compass is used to discover the numerical sequence. It takes five branches to spiral around the trunk twice to complete another pattern.

MATH POSSE | PAGE 9

Are known for its majestic multicolored feathers. Behind this feather are pieces of evidence form of a complex pattern of spirals in opposite directions. This pattern has inspired the possible manipulation at a molecular level.

R E P R E S E N T A T I O N S

M A T H

I N

O F

N A T U R E

PRODUCING THE BAD DIFFICULT AND THE GOOD EASY THE GOLDEN RATIO If the Fibonacci sequence simply talks about the surface of the patterns, the golden ratio touches on the emergence of the latter, as well as the proportionality and ratio. Here are a few of the examples: ANIMAL BODIES Looking at the complexity of the animals, we can see the presence of the golden ratio numbers. The value from the top of the head to the navel and from the navel to the floor can be ratioed with each other. SEED HEADS The Fibonaccian sequence, though unnoticeable, is present in the flowers, typically the seeds in the center. These spiraling patterns are exhibited from the center and spread through. HURRICANES At a single glance, everyone can agree how a hurricane particularly presents the Fibonacci sequence. Some more examples are the animal flight patterns, shells, spiral galaxies, branches of a tree, pine cones, flower petals, and reproductive dynamics.

"The golden ratio is a reminder of the relatedness of the created world to the perfection of its source and of its potential future evolution." Robert Lawlor

MATH POSSE | PAGE 10

Also known as the "Rule of Thirds," the golden ratio, aside from the complicated paragraphs of mathematical figures, is confined within nature. To put it simply with the definition of this given representation, two certain numbers are considered to be in ratio with each other if the sum of these two numbers, when divided with the larger number, is in proportion with the value of the quotient of these numbers (the larger number divided by the smaller one). It is not restricted to mathematical figures as its importance extends in nature where it improves the physical form of the organisms. For certain, it does foster and puts on view natural-looking compositions of the pattern that are beyond attractive to the bare eyes. The golden ratio is described to share the same characteristics as that of a fractal (see next page) which plays a significant role in conveying an aesthetically pleasing presence in the surroundings.

R E P R E S E N T A T I O N S

M A T H

I N

O F

N A T U R E

A WAY OF SEEING INFINITY FRACTALS

"Fractal geometry is not just a chapter of mathematics, but one that helps every man to see the same world differently." This quotation by Benoit Mandelbrot utters the irony of seeing the same world in a more distinguished way.

MATH POSSE | PAGE 11

IS THAT POSSIBLE? Out of all the biological representations of mathematics in nature, the most fascinating yet to be described are the patterns exhibited by fractals. A fractal is a member of the geometrical shapes that is just unbelievably, infinitely complex. As best believed by the mass, math is everywhere to the extent that these fractals actually are surrounding us, even though it may not seem visible to the eyes. First off, before digging through the surface of the matter, one of the fractals we see most often is the Mandelbrot set, named after a renowned mathematician, Benoit Mandelbrot, who coined the term 'fractal' himself. The English word was derived from the Latin word fractus described as "broken" or "fractured"– which ludicrously is not what infinite means. As playful as the meanings can get, that is exactly how fractals display themselves in a physical manner. To make this more interesting, it is in our greatest honor to disclose how unique fractals are in every way possible, whenever we see them in nature. Moreover, they as well exist everywhere in this natural world! We see them in trees, with the main trunk as their origin, subsequently making their ways by growing branches and twigs of their own, and that goes on. This cycle, for example, creates a different pattern, an infinite one. To simply put, fractals reproduce these patterns by fabricating the resemblance from the precedence, starting on a smaller scale.

Life is a pattern, they say. Well, so is mathematics! Like humans re-experiencing a certain event in their lives, fractals start from simple patterns that reproduce to more complex ones. One of the most usual examples to be given is the snowflakes that fall from the cold breeze of the sky. Another one is the elegance of the flowers that bloom from their seeds to enchanting ornaments of their own. Lastly, exploring through the forest of tall trees and the wildlife, under the scorching heat of the sun, we can try looking up and from a shade and see the patterns of the branches crawling from one point to another. And there they go, repeating the cycle until we lose track of where is what.

"TO UNDERSTAND THE UNIVERSE, YOU MUST UNDERSTAND THE LANGUAGE IN WHICH IT'S WRITTEN, THE LANGUAGE OF MATHEMATICS." GALILEO GALILEI

Sources

MATH POSSE | PAGE 12

Britannica, T. Editors of Encyclopaedia (2019, March 18). Mayon Volcano. Encyclopedia Britannica. https://www.britannica.com/place/Mayon-Volcano Dvorsky, G. (2017). 14 Interesting Examples of the Golden Ratio in Nature. Mathnasium. https://www.mathnasium.com/examples-of-the-golden-ratio-in-nature Ghose, T. (2022). What is the Fibonacci sequence? Live Science. https://www.livescience.com/37470-fibonacci sequence.html Haak, D. (n.d.). Spherical symmetry: Definition, biology & animals. Study.com. https://study.com/academy/lesson/spherical-symmetry-definition-biology-animals.html Iternal (n.d.). What is a fractal?. Iternal. https://iternal.us/what-is-a-fractal/ Lal, D. (2015). Geometry and Geometrical Patterns in Nature. The Signage. http://www.thesignage.co.in/PDF_July2015/Geometry%20and%20Geometrical%20Patterns%20in%20 Nature_1.pdf Livio, M. (2020). Symmetry and the Laws of Nature. Psychology Today. https://www.psychologytoday.com/us/blog/why/202010/symmetry-and-the-laws-nature Meisner, G. (2012). The Human Face and the Golden Ratio. Golden Number. https://www.goldennumber.net/face/ Mikell, M. (n.d.). Radial symmetry: Definition, biology & animals. Study.com. https://study.com/academy/lesson/radical-symmetry-in-biology-definition-examples.html New World Encyclopedia (n.d.). Symmetry (biology). New World Encyclopedia. https://www.newworldencyclopedia.org/entry/Symmetry_(biology) Seiglie, M. (2021). How the Amazing Peacock's Feather Refutes Evolution. United Church of God. https://www.ucg.org/members/compass-check/how-the-amazing-peacocks-feather-refutes-evolution The Oak. (n.d.). La Quercia. https://www.la-quercia-institute.com/about-us/the-oak/ Thomas, R. (n.d.). The Fibonacci sequence: A brief introduction. Plus. https://plus.maths.org/content/fibonacci sequence-brief-introduction Wallenfeldt, J. (2018, March 15). Fingal’s Cave. Encyclopedia Britannica. https://www.britannica.com/place/Fingals-Cave

FROM THE EDITORS

Although, on the other hand, it should be best believed that mathematics is not simply connected to nature, as it is found in nature itself. The patterns we see and stare at from moment to moment indicate the different sequential reproduction of the mathematical concepts which we should learn about. Mathematicians or scientists assert that the field does not talk about merely organizing statistical data; thus, they also honor the act of reflecting these mathematical connections, relationships, and conceptions to the natural and physical world– that inside a certain connection lies another one. If mathematics is all about patterns, then so are our lives. When people utter that math is everywhere, it does not pertain to computations being done here and there but instead, the statement speaks of both the abstract and concrete shreds of evidence it shows in nature. Finally, learning mathematics in the natural spheres gives us a wider grasp of the real world and understanding its realms.

MATH POSSE | PAGE 13

A French Egyptologist and the legendary mystic who popularized the pseudoarchaeological idea of sacred geometry, particularly in Ancient Egypt, R. A. Schwaller de Lubicz, quoted: "The golden number is a mathematical definition of a proportional function which all of the nature obeys, whether it be a mollusk shell, the leaves of plants, the proportions of the animal body, the skeleton of a human, or the ages of growth in man." First off, straightforwardly, it should be debunked by now, the general misconception that the word mathematics is alone observed during our educational years because the truth is that humans are experiencing the concepts incorporated with mathematics on a daily basis. Technically, the word is defined as the "abstract science of numbers, quantity, and space". The things we see with our bare eyes may indicate different things, but observed more carefully and analytically, we can then realize that this is what mathematics is being taught for, and most of all, we will learn that aside from its scientific composition like chemicals, compounds, molecules, elements, etc., the natural world also introduces the existence of mathematics not just in their external, extended to the internal characteristics. As vital as the role of mathematics in nature is, it is just as critical to learning about their connection.

FROM THE EDITORS

When we hear the word mathematics, what we always thought is numbers. Some people might feel nauseous when they see problem equations, but as we try to visualize it with nature, it makes math more interesting than just a number that is needed to be solved, as we also discover something about nature.

As we now know and understand more about the connection of mathematics in nature, we witness and appreciate more of its beauty. That is why I would like to inform everyone that by studying math with pleasure and honing our skills, we are already contributing something to the world, which will improve the quality of life. With mathematics and nature, we can produce great things and discover more of their beauty; as we apply them according to our profession. We notice that in nature, there are orders and patterns. It is the same with mathematics, which is known as an organized knowledge structure of numbers. Due to these orders, life is balanced, and we also get to experience the natural world. As we further discover in math that everything in this world is interconnected, we fail to think that we are also part of it.

MATH POSSE | PAGE 14

The five representational has shown us patterns that suggest how deep the connection between mathematics and nature is. We might not realize it, but Mathematics is everything, and everywhere, it is always seen, with nature. Without it, we wouldn’t understand how everything in this world works. Changing one’s perspective on learning mathematics would be meaningful and understandable if related to nature. Nature is a rational representation of mathematics as how will one see its importance and makes sense in our lives.

Mathematics has made a significant contribution to our way of life, especially now that we live in a technologically advanced society. The world develops as we apply our maths skills, together with inspired ideas from nature, we can create beautiful things such as architectural design, appliances, technologies, transportation, and many more. For that reason, we are now living a more comfortable and convenient life.

MATH POSSE VOL. 08 | MARCH 2022