BARAZON, PAULINE KAYE ORTEGA, ENRICO

MARCH 2022

MATH MATHEMATICS

IN NATURE GEOMETRICAL SHAPES, SYMMETRY, FIBONACCI SEQUENCE, GOLDEN RATIO, & FRACTALS

Did You Know? The iCloud logo was made with the consideration of the Golden ratio. The Hindu-Arabic Numeral system got known became popular because of Leonardo Fibonacci, the finder of Fibonacci sequence. There are 5 patterns in nature; spiral, meander, explosion, packing and branching. Tiny bubbles formed by soap and water can be considered an example of fractal.

Lynn Arthur Steen, an American mathematician and former professor of mathematics at Olaf College, Northfield, Minnesota in the U.S. states. stated that Mathematics is the science of patterns.

CONTENT Cover Page Trivia: Did You Know? Content Geometrical Shapes

Page 4 – 6

Symmetry

Page 7–9

Fibonacci Sequence

Page 10-11

The Golden Ratio

Page 12-14

Fractals

Page 15–16

Authors’ Insights

Page 17

GEOMETRICAL SHAPES

Geometric shapes are the figures we

see in our daily life. These are the

figures like squares, circles, rectangles,

triangles and etc. Geometric shapes in

math can by 2d shapes and 3d.



There are many Geometric shapes in

nature that people do not see. Here's an

example of Geometric shapes in nature.

Snowflakes There are different types of snowflakes.

The most basic snowflakes is the

hexagonal prism, it is snow crystal

geometry that shows thin hexagonal

plates and columns.

Hexagonal Prism

A hexagonal prism has a hexagonal base and top. This three dimensional

shape has 8 faces, 18 edges, and 12 vertices. There are 6 are rectangles in 8

faces and 2 are hexagons.

Snowflakes has a significant and perfect geometrical shapes. The common

snowflakes is the stellar plates that has a form that is similar to star shape.

Snowflakes are one of the example of geometric shapes in nature, it shows

the different types of shapes. It can be also an example of symmetry since

the shape of snowflakes has repetition.

Rakotzsee in Gablenz, Germany

Shapes

etrical m

G eo . e r

Heavy monsoon storms.

palm oil plantation

a in N tu

Thailand's Pathum Thani province.

Trees

SY Symmetry is one of

patterns that people see in

nature. There is repetition

of the pattern element that

can be either reflection or

rotation.

RY

E M T M

Mountains Symmetry is an element

that reflects, rotates,

translates. It can make a

similar shape, form, and

patterns in multiple lines

of symmetry.

The reflection of the mountain in the sea is similar to a person looking at the

mirror. The upside-down version of the mountain creates a reflection that is

symmetrical.

Symmetry is in music & arts, architecture,

literature, history and nature

Symmetry can be also seen in

Starfish Starfish has a pentameral symmetry

Jellyfish Jellyfish has a radial symmetry

sea anemone Sea Anemone has a radial symmetry

i S c e c q a u n ence o b i F

Fibonacci Sequence is numbers that can be found everywhere in the world. Nature is all about math and everyday, we see trees and flowers everywhere in our environment. The trunk of the trees shows fibonacci spirals as the tree gets taller. The petals of a flower such as sunflower, which is the common example of fibonacci sequence in nature. The flower grow with the Fibonacci.

Fibonacci Sequence is a pattern that we see in nature. Observing the flowers and trees it shows and follow the Fibonacci sequence. It appears the arrangement of the spirals in trunk of the trees and petals of flowers. The human body such as face, body, and hands

shows Fibonacci Sequence proportions.

11

The Golden Ratio The golden ratio is a special number equal to 1.618. It can be seen in Mathematics, Arts, Geometry and in nature showing a visual aesthetic that is pleasing to the eye.

It is also called

The Golden Ratio is considered the most beautiful number because it can be found or seen everywhere not only in geometry or mathematics but anywhere in nature itself.

"The Divine Proportion" The Golden Ratio



The Golden Ratio computation translation: The longer part divided by the shorter one

The sum of longer and shorter divided by the longer part

This can be used in making 1.618... various shapes and forms





A A B

B A B

A

1.618...

12

GOLDEN RATIO in NATURE The Golden Ratio can be seen in almost any element of nature. It can be seen in land forms, plants and trees, animals, people, foods and even weather and so on.





It creates different forms of spiral making the Golden Ratio related to the Fibonacci Sequence.

The Golden Ratio can also be generated or created by natural events and activities such as ocean/sea waves and hurricane.





Egg haha

13



H U M A N P R O P O R TI O N S

Each part of the human body has a subsequent representation of the Golden Ratio such as the navel, legs, arm, core, face etc.

Even the least visible ones like fingerprints are unexpected to represent Golden Ratio.



TRIVIA : Did you know? The Golden Ratio inspired artists like Leonardo da Vinci and Michaelangelo influencing their artworks.

Mona Lisa by Leonardo da Vinci

14

FR CT LS Fractal is a continuous repetition of similar patterns without an endpoint.

Fractals patterns are basic and yet creative because they show a progressive design.

Fractals are seen in nature such as plants, snow or ice and even in humans and light storms.

15

Koch Snowflake The Koch snowflake in particular gradually duplicates similar patterns.



L I G H T S T O R M

The fractal pattern seen in this light storm is the forked lightning of the thunderstruck.

Like this leaf, it has small continuous roots similar to a tree where fractals can be seen in the branches.



I N K A N S A

The visible fractal that can be seen in humans are the veins.

16

"Why do you need to learn the connection of mathematics with our nature?" Mathematics is the foundation of everything developed by our ancestors up to this time. Maybe then the methods and discoveries about the inventions or creations of our ancestors were not really advanced but the development of their lives and the world is becoming progressive because they applied and their discoveries and acted out of curiosity to prosper. The application of mathematics to life and the world is the result of new discoveries and solutions about specific and certain things. It brings us to modernity that we humans, animals and the nature benefit from; we are able to determine what is right and wrong, what is safe and dangerous, what should and should not be done and more. Most importantly, learning math and understanding it helps us to understand the world better.

17

- Ortega, Enrico Miguel

Mathematics in nature shows the true essence of Mathematics in the modern world. We do not see the details in simple leaves, flowers, mountains, and animals. But if we give our attention to small details we can appreciate such a masterpiece. Some people see math as a problem and it is just full of numbers and computation. But, if people can learn and understand that mathematics makes our surroundings meaningful and significant, they will appreciate that mathematics is important in nature. As an architecture student, it is important for me to always check the details of every design and see the beauty of patterns of every object. Mathematics shows me that I need to follow certain patterns to be able to explore and understand. The connection of mathematics in nature gives us the idea that one shape is connected to another object that can build a masterpiece. Without Mathematics in nature, there will be no patterns and we will not be able to communicate using illustration. - Barazon, Pauline Kaye

MARCH 2022

S

C I T RE A EMATU H T N GEOMETRICAL SHAPES, A IN M SYMMETRY, FIBONACCI

SEQUENCE, GOLDEN RATIO, & FRACTALS

YE : RS E KA O IN TH AU PAUL ICO N, ZO ENR A , R BA EGA T R O