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MATHEMATICS NATURE EDITION

EXPLORING

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EXCLUSIVE THE

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Interview with our special guests ISABELI CAPIRAL Author & Editor

NICHOLE GILMORE Author & Editor

P PR RO OJ JE EC CT T Y Y

Hi guys, I'm Flame Princess and Welcome to planet math! Wherein you will discover the fascinating side of mathematics that you possibly never know exists. Yep, you read it right! the compelling beauty of mathematics, besides its practical equations, formulas, and numbers that we already know in school. In planet math, you will have a chance to meet your favorite cartoon characters that will guide you in exploring the fun sides of mathematics, specifically in the sense of nature. So what are we waiting for? let's begin our exploring journey! and start learning.

What's up you'll it's your girl, Marceline! the vampire queen. Come and join us to travel around on the planet math! Here in math planet, we will discover how math is not only about numbers or problemsolving but it shows how mathematics makes nature so marvelous. Nowadays kids hate math but it is time to change that. Mathematics is everywhere and it is essential to know the beauty of it. I'm here with one of your favorite cartoons throughout the journey, this is your chance to meet them. What are you waiting for let's go!!!

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Editors' note.................. page 2 table of contents...........page 3 All about Geometry................................. page 4 Uncovering Geometry of the world.......page 5

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Fascinating Symmetry in nature........... page 6 Cool examples of Symmetry in nature..page 7

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The Divine proportion............................ page 10 Manifestations of golden ratio..............page 11

Fibonacci Spotted in nature................... page 8 The Nature's Secret code........................page 9

Amazing world of Fractals................... page 12 Fractals in nature....................................page 13 Special Guests........................................ page 14 Authors' Reflections...............................page 13

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LEGO LAND

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THE BEARS' CRIB

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STEVEN'S UNIVERSE

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TOWNSVILLE

CLARENCE STREET

TITANS TOWER

GEOMETRY Definition Geometry is the branch of mathematics concerned with an object's shape, size, dimensionality, and spatial relationships with other properties in space. In this field, we learn about angles, points, planes, measurements, transformation, and such matters substantial in our everyday life.

Check Out! "Everything is awesome" song from the Lego movie

Brief History The crucial need to measure shapes gives birth to geometry. In the early 6th century BCE, Greeks have developed principles and extensive knowledge on the concept of abstract measuring that led to the mathematical discipline of geometry. Its name derives from the Greek word geo, which means "earth" and metron "measure.", implying the measurement of the Earth. Euclid of Alexandria (325-265 BC) is one of the most notable Greek contributors to the study of geometry as he established a 13-book treatise entitled " Elements." that bought substantial impacts on the development of western civilization and even in our modern disciplines of geometry such as art, science, architecture, engineering, etc. Hence from his significant contributions and knowledge in the course, he is regarded as the "father of geometry."

https://fineartamerica.com/featured/euclid-ancient-greekmathematician-science-source.html?product=fleeceblanket&blanketType=blanket-coral-50-60

https://www.britannica.com/science/geometry

Euclid FATHER OF GEOMETRY

- "The Laws of Nature are but the mathematical thoughts of God."

https://www.britannica.com/science/geometry http://www.thegeodes.com/templates/geometryhistory.asp

measurements of the earth

UNCOVERING

GEOMETRY OF THE WORLD triangles are three side polygons, and it is the first geometric shape that can form with few lines. As above, of the palm oil plantation in Indonesia, there are four equilateral triangles. Equilateral triangles are also called perfect triangles, with all three sides being identical in length.

spheres are three-dimensional figures that are abundant in nature. We see through the tiniest droplet to the perfect shape of the sun. Unlike the moon and earth, they look like squashed spheres on the top; these are called oblate spheres. As an example, a picture of a supermoon that captured in September of 2015.

angles are figures with two rays sharing a common endpoint. In every corner of nature, angles are always present. A starfish is a perfect model for angles. A five-armed starfish has approximately 89.69 degrees angles.

Rectangless

are 2-dimensional shapes; a quadrilateral is four sides in a plane with 90 degrees angles on every side. Rectangles are rare in nature. A photo of Tessellated pavement in Tasmania, Australia, is a perfect example of rectangles present in nature. Despite it looking distinctly artificial, they are a natural occurrence of erosion.

Fascinating

Symmetry in nature

definition Symmetry is a fundamental part of geometry that portrays the balanced proportions found on two or more dimensions of an object, meaning half of an image is like a reflection on its other half. Its shape remains consistent whether rotated, flipped, or moved, depicting an equal distribution of its parts. The manifestation of symmetry is visibly evident in our natural world, from the field of sciences to the disciplines of arts, there is a harmony of patterns or shapes among tangible matters and animate beings. Hence the sense of symmetry has been substantially relevant to human life, as it allows us to build innovative creations by recognizing the fascinating connection among the elements in our world and its spectacular beauty that makes us reflect how clever our world is connected and well made. https://byjus.com/maths/symmetry/ https://www.nias.res.in/publication/philosophy-symmetry

Line of symmetry

refers to the imaginary line or axis that runs through the center of an object, which allows us to visualize the symmetrical halves of a particular figure. this is an example of "line of symmetry" in a square and as you can see, it has equal proportions of a triangle, making it a symmetrical figure. Mind blowing isn't it? Wait till you see the cool examples of symmetry in nature.

Reflectional Symmetry Reflectional symmetry is also known as bilateral symmetry. As if there is a line in between that divides the symmetry with the reflection of the other half. An ideal reflectional symmetry in nature is butterflies, as it has an identical pattern - each wing. 8in 4 3 1 6



Translational Symmetry Translational symmetry is the repeating / tics i l o d-p n a omy rfly n o tte /ec u m b o g.c rch a a m n i /ws the-mo / : s http r-andde mur

pattern of a particular shape, translated into another location without the changes in its sole structure. Honeycombs have a recurrent hexagonal structure that can hold as many queen bee's eggs and pollen and honey as the worker bees bring.

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Helical Symmetry

Helical symmetry is a synchronized pattern in threedimensional space that can be translated and rotated either towards or away from the central vertical axis. An ideal spiral symmetry that can see in nature is an Aloe Polyphylla plant. The stemless aloes have a distinctive spiral shape that either grows in a counterclockwise or clockwise way.



Rotational Symmetry

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The structure is a rotational or radial symmetry if it has an exact duplication of parts repeated around its central axis. Jellyfish is one of the representations of radial symmetry in nature. It has a luminescent radial pattern above its bell.

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Trees are one of the main components of nature; Fibonacci lies with branches of the trees. Fibonacci begins with how branches grow from their main trunk creating two more points. In one of the new stems, there will be another two spouts out of it, and then the stems stay dormant.

There is a fascinating way on how bees follow Fibonacci. Honey bees use the Fibonacci sequence as a familiar reproductive pattern, If the male bee fertilizes an egg, it will be a female worker bee, which means they have two parents. If the egg is not fertilized, it will produce a male bee or a bob, which only has one parent. As the family tree continues to grow, the Fibonacci sequence will be 1,1,2,3,5, and so on.

FIBONACCI nature spotted in

Pine cones have a similar Fibonacci sequence with the reproductive pattern of honey bees. The seed pods on the pine cone are arranged in a spiral pattern. Each seedpod spiraled outward from the center. The number of spirals in the pine cone is a Fibonacci sequence, in which the numbering pattern is 1,1,2,3,5,8, etc.

Tigers are considered majestic because of their perfect face. The Fibonacci sequence also lies underneath its facial structure. Like any animal body structure, the tiger's face has the golden ratio measurements of its width and length.

NATURE'S SECRET CODE

The

Fibonacci Spiral Fibonacci sequences are also represented in a spiral manner to portray the patterns of Fibonacci numbers. It can be formed by constructing a rectangle with an area of 1.618 or known as the golden ratio, then is proportioned into two (1x1) squares, forming a proportion of (2x2) squares, then further proportion of squares until it equates to the area of the rectangle.

https://www.cuemath.com/numbers/fibonacci-sequence/

is a series of numbers whereby each number is the sum of two digits preceding it, starting from 0 and 1 until it became like this: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 and so on with a mathematical equation expressed as: Fn = Fn-1 + Fn-2, where n represents the nth term.

https://www.livescience.com/37470-fibonacci-sequence.html

Fibonacci Sequence

Still doesn't make sense?, well here's an easy representations of Fibonacci spirals that we probably haven't recognized

Leonardo Pisano Fibonacci Leonardo Fibonacci is an Italian number theorist who introduced the concept of Fibonacci numbers, sequence, and other math courses such as the Arabic numbering system, Square numbers, and the practice of geometry that are integral in our lives today. He is known for his excellent published works, specifically "Liber Abaci." in 1201, which translates to "the book of calculations.", this book is encouraging Italian merchants to use the Hindu-Arabic numerals for the efficiency of their business processes and systematic approach on handling profits. With this book, he also presented the sense of Fibonacci sequence and numbers in relevance with his discussions about predicting number patterns (the bunny problem). https://science.jrank. org/pages/2705/Fibo nacci-SequenceHistory

these are also the representations of the golden ration, which will be learning next ->

mind blowing right? with these ubiquitous representations of Fibonacci in nature, it is often termed as Nature's secret

code

https://science.howstuffworks.com/math-concepts/fibonaccinature.htm

THE DIVINE PROPORTION Definition The Golden ratio is a irrational number approximately equal to 1.618 or sometimes known as phi value, since it is represented using the Greek letter phi, Φ. To simply put, the golden ratio results when dividing a line segment into two smaller parts of different lengths: long (a), short (b), in which the ratio of the whole line segment to the longer part (a) is equal to the ratio of the longer part to the shorter part (a+b). The golden ratio is closely associated with the famous Fibonacci numbers, whereby the ratio of two Fibonacci numbers gets adjacent to the golden ratio as it increases. https://www.masterclass.com/articles/golden-ratio-explained#how-to-calculate-the-golden-ratio

Brief Time-line History

1509 AD

300 BC

EUCLID Euclid, or as we now know, "the father of geometry." is the first mathematician who defined the concept of the golden ratio in his famous book entitled the "elements." whereby at the time, he named it as the "extreme and mean ratio."

LUCA PACIOLIFURTHER

1835

MARTIN OHM

1910

MARK BARR

Paciolifurther is an Italian Ohm is a German Barr is an American mathematician who integrated mathematician who mathematician who the concept of the golden ratio determined these first used the Greek with its connection to the natural concepts of ratio and letter phi (ϕ) to world that he further examined proportion to be "golden.", express the golden in his book called "De Divina wherein he uses the term ratio. Proportione." which translates to "goldener schnitt." which "On the divine proportion." translates to "golden illustrated by famous Leonardo section." Da Vinci. hhttps://www.britannica.com/science/golden-ratio

https://www.masterclass.com/articles/golden-ratio-explained#how-to-calculate-the-golden-ratio

The Divine proportion The golden ratio is also referred to as the "divine proportion" because of its evident ambiquitous commonness in the natural world. It exists throughout artworks, science, architecture, nature, and even in our human body that we haven't quite realized yet. For instance, the spiral arrangement of flower petals often follows a golden ratio, the distance between our eyes, nose, and lips is in proportion with the golden ratio, the spiral pattern of our hurricanes is also relative to the golden ratio, and much more visible manifestation of the golden ratio in our natural world. https://www.nationalgeographic.org/media/golden-ratio

Nautilus shells The Nautilus shells are prominent in golden ratio because they follow the logarithmic spiral. Fun fact it is not entirely true multiple researchers prove it is a myth. Researchers measures numerous nautilus shells, and as a result, it does not generally follow the 4:3 ratio but on the average of 1.310. https://link.springer.com/article/10.1007/s00004-018-04193#:~:text=Meisner%20(2014)%20alternatively%20suggests%20that,root%20of%20the%20golden%20ratio).

Fiddlehead fern The fiddlehead fern has a spiral structure on its tip because its midrib expands as it spirals toward the base of the stalk. The structure of the fiddlehead follows the golden ratio approximately. https://smokymountainnews.com/archives/item/17427-gracefulferns-a-fiddling

The arch of the ocean waves The golden ratio can also see in the ocean waves. The wind blows the surface of the ocean creates a wave crest. The waveshape must be shifted to 90 degrees to conform to the golden ratio.

https://expertphotography.com/golden-ratio-photography /#:~:text=The%20golden%20ratio%20is%201.618,composition%20from%20good%20to%20excellent.

Chameleon's tail

Chameleon is well-known for its shifting color and perfect curly tails. Their perfect curly tails depict the golden ratio. They curl their tails to hold and balance themselves in branches, to carry objects, to look smaller, and can express their mood. https://oddlycutepets.com/why-do-chameleons-curl-theirtails/#:~:text=Chameleons%20curl%20their%20tails%20to,and%20to%20 express%20their%20mood.

Amazing World of Fractals Definition

Fractals are infinitely complex patterns that are equal for all scales regardless of what perspectives they viewed in, they will remain the same to the whole figure. They are formed in a simple repetitive manner in an ongoing feedback loop, as they widely exists between the familiar dimensions of our natural world. A shape doesn't have to be exactly identical to be classified as Fractals, as long as it displays the main conditions of inherent and repeating similarities, it is classified as fractals.

Benoit Mandelbrot

Mandelbrot is a mathematician who coined the term fractal, derived from the Latin word "fractus." which translates to "fragmented or broken." considering that there are fractional components within each Fractal. He was the first to point out that fractals could be an ideal tool in applied mathematics for modeling a variety of phenomena from physical objects to the behavior of the stock market. https://www.britannica.com/science/fractal

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Find the five hidden words that can be considered as representations of fractals in nature

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Romanesco Broccoli

If you like eating vegetables and fruits such as pineapples or salad, without even knowing, they are an example of fractals. Romanesco broccoli has a breathtaking structure of spires that depicts fractals. The shoots of the broccoli shoot buds at a rapid pace which elevates the tip away from the center, which creates a conical structure.

Snowflake

In each snowflake, there is a unique structure associated with fractals. The Kock snowflake is a diagram that is similar to a real snowflake. Fractals are present at the center of the snowflake as the crystal formation expands outward.

Lightning

A lightning bolt is a naturally occurring fractal pattern. A bolt of lightning happens when an amount of electrical charge subdue the air's insulating properties. In the process of overcoming that breaks through the air with electricity. In this process, the lightning creates a fractal pattern through the air.

Spider Web

Fractals are also can see in the spider web in its hypnotizing pattern. Spider has a circular pattern to lure its prey to their death trap. The most common type of web that spiders make is the orb web.

exclusive!!!

Interview with the Justice League NAME: Danielle Patrick, Ang

AGE:19 AFFILIATION: SHS Classmate

1. The content of the magazine contains a lot of detailed information. 2. I appreciated how they design their magazine, I used to love cartoons and it just brings back memories 3. I see mathematics as thrilling subject to tackle, and the magazine matches the vibes of its content

NAME: Shane, Dino AGE:19 AFFILIATION: SHS Classmate 1. The magazine is extremely good. The information about how math and nature relate to each other is clearly presented, and the designs aid in clarifying the type of information being read. 2. I really like how mathematics was linked to nature because its beauty is based on harmony, patterns, and symmetry. 3. Math is a difficult subject for me, but I've realized that it's more than just formulas, numbers, concepts, volume, and systems. Math, like art and music, has the ability to be beautiful.

NAME: Alexandra Camilla, Villarama AGE: 19

AFFILIATION: JHS Batchmate

1. Upon viewing the magazine, it looks interesting. The contents were comprehensive and organized. The context was neat. 2. I appreciate math's relation in nature, it fascinates me and encourages me to learn about it more. 3. Usually, math is something hard for me. Something I'd want to ignore, but scrolling through the magazine, it sure looks fun as well and it also shows me that there's more in mathematics other than formulas and equations.

NAME: Erica Jane, Andag AGE: 19

AFFILIATION: SHS Classmate

1. I appreciate the visuals and creativity of the design of the work. 2.The content of the magazine enlightened me that mathematics is not something we learn for nothing but it is related to how the world works 3. I appreciated how mathematics can be applied to practicality. I was a student who questions how mathematics can be useful for me when I cannot perceive it as something that is related to the profession that I want to pursue.

WHY DO YOU NEED TO LEARN THE CONNECTION OF MATHEMATICS WITH OUR NATURE?

AUTHOR: Isabeli I. Capiral

AUTHOR: Nichole G. Gilmore

Learning the sense of math in nature is essential in our lives because it substantially helps us better understand the world. Through the five topics we've discussed in our magazine, I perceive how evident the manifestations of math are in everyday lives. From the patterns of nature, dimensions of arts, architecture, and even in the processes of the human body, there is the inevitable presence of math around us. Hence, humans need to learn how to recognize these patterns and connections of nature because, in the same relevance, it allows us to understand math in a broader sense, which I believe is vital for today's generation. I think it is time we stop confiding math being exclusive to numbers, equations, and formulas because math is more than these concepts. It is beautiful, creative, and academically satisfying as the process of math itself is compellingly bright. Understanding math in nature or perceiving math beyond our limited mindset will allow us to expand our full potential in being creative, innovative, and flexible in adapting to such change. Analyzing its patterns and connections develops our logical reasoning in figuring out ways to handle a particular matter. Moreover, it enables us to discover, experiment, and envision broader results by making connections and sense to what we see.To sum it up, learning the sense of math in nature is vital to humans as our lives are full of tangible and intangible patterns. Recognizing them will lead us to understand the world better because we're able to connect things as a relation of a whole, make sense of our surroundings, and innovate remarkable things as we expand our potential to create.

It is essential to know the interconnection of mathematics in nature. Nature can be understood in mathematics. To understand how the worlds work, that everything takes in shapes, and to perceive its purpose nature. With math, we can also unravel the mystery of forms of nature and how everything takes in shapes. In nature, we learn that math is everywhere without even knowing it gives purpose to how things should be. We are always in the presence of mathematics, and we need to understand and recognize its contribution to nature. We see some mathematical concepts and patterns that make nature authentic and meticulous. We notice that the earth is a sphere, how volcanos take the shape of a cone, why the chameleon tail is spiral, with these questions will answer through understanding mathematics. We grew up that it is difficult to understand math, lose interest in it, and fixed our mindset that it is all about numbers, computations, and solving. It is time to change our perspective towards mathematics and acknowledge that we are part of it. Consequently, mathematics lies under nature which defines why everything takes in shapes. Mathematical patterns, sequences, and ratios are what nature elucidates its structure. The significance of learning the relevance of mathematics and nature is to acknowledge how everything makes sense. Understanding nature through math gives us ideas to develop as humans to understand how the world make better.

THE LAWS OF NATURE ARE BUT THE MATHEMATICAL THOUGHTS OF - Euclid GOD