MATH IN NATURE

Play Game

SeePresentation

Team

Math in Nature

Proportion and Graph in Nature

Team and Backstage

Parallel and Meridian in Nature

Thanks and Let's Play a Game

Let's watchFrom Our StudentsLet's try

Interesting

Math in Outer Space

Concentric Circles in Nature

Hexagons inNature

Fractals in Nature

Human andGolden Ratio

Golden Ratio

The Fibonacci Sequence

Intro

CONTENTS

Have you ever stopped to look around and notice all the amazing shapes and patterns we see in the world around us? Mathematics forms the building blocks of the natural world and can be seen in stunning ways. Let's go we look together.

Named for the famous mathematician, Leonardo Fibonacci, this number sequence is a simple, yet profound pattern. Based on Fibonacci’s ‘rabbit problem,’ this sequence begins with the numbers 1 and 1, and then each subsequent number is found by adding the two previous numbers. Therefore, after 1 and 1, the next number is 2 (1+1). The next number is 3 (1+2) and then 5 (2+3) and so on.What’s remarkable is that the numbers in the sequence are often seen in nature.

The Fibonacci Sequence in Nature

a few examples

When a Fibonacci number is divided by the number that precedes it, it converges to the golden ratio, an irrational number (1.6180339887). When the golden ratio is applied as a growth factor, the familiar logarithmic spiral appears below.

Golden Ratio in Nature

When the spiral folds in the structure of snails are transferred to a piece of paper, a rectangle emerges. This shape with the ratio of the sides equal to the golden ratio is called the "golden rectangle". When combined with squares as in the figure on the right, a spiral emerges. It is possible to see these spirals, which are based on the golden ratio, on sunflowers or cones, especially snails.

When the structure of the sea shells is examined, the inner surface is smooth, the outer surface is grooved and the folds that progress from the bottom to the tip are noticeable. The tangent of this curvature in each fold of the seashell, called the logarithmic spiral, also corresponds to the golden ratio.

Let's we look there where golden ratio in nature

No two snow crystals are alike. And all have hundreds of golden ratios.

Although it is generally too small to be seen by the eye, the ratio of various protrusions always gives the golden ratio in the short and long branches forming the snow crystal.

When the number of female bees living in beehives is divided by the number of male bees, the golden ratio emerges.

Let's we look there where golden ratio in nature

pyramid spiral aloe spider web ocean wavescauliflower and MORE...

chameleon comfrey flower daisy nautilus shell

Let's we look there where golden ratio in nature

You will see that many organs in our body have values ​​at or close to the golden ratio. When we look at the ideal human face used by sculptors or painters, we see these proportions everywhere. When we look at some people in our daily life, their face or body is aesthetic, even if they are not very handsome or beautiful. It has been seen that these people generally have lines with a golden ratio.

Like everything in nature, there is a golden ratio in the human body. The human body is enormous when viewed from an aesthetic point of view thanks to the golden ratio. That's why artists have been inspired by the human body throughout history. This ratio is present in almost every part of the human body. So when you take the body as a whole or just look at your organs, you will see the golden ratio.

HUMAN AND GOLDEN RATIO

When you look at your body, if you compare the distance from your whole body to your feet to your belly, you will find the golden ratio. Likewise, the ratio of the distance between your navel to your vertex and the distance between your shoulders and vertex corresponds to 1.618. If you look at the ratio of the distance from your navel to your knee and the distance from your knee to the ground, you will again see that it is the golden ratio.

Like everything in nature, there is a golden ratio in the human body. The human body is enormous when viewed from an aesthetic point of view thanks to the golden ratio. That's why artists have been inspired by the human body throughout history. This ratio is present in almost every part of the human body. So when you take the body as a whole or just look at your organs, you will see the golden ratio.

HUMAN AND GOLDEN RATIO

The fingers have three knuckles. When you look at the knuckles, the ratio between the first two knuckles and the length of your finger is the golden ratio. The ratio between the middle finger and the little finger is the golden ratio. The ratio of the wrists from the elbow to the distance between the wrists and the fingers is the golden ratio. There is a golden ratio between the length and width of the face. There is a golden ratio between mouth and nose width.

Some of the golden ratios in the aesthetically ideal human body are as follows:

HUMAN AND GOLDEN RATIO

*The width of the nose and the width of the nostrils is the golden ratio. *The golden ratio is the ratio of the distance between the eyebrows of the pupils to each other. *There is a golden ratio between the width and length of the upper two teeth. *Apart from these, the length of the parts of the trachea divided into the right lung and the left lung are not equal. It is shorter due to the heart on the left. When you compare the two, the golden ratio comes out. This ratio is encountered even when looking at the DNA structure.

Some of the golden ratios in the aesthetically ideal human body are as follows:

HUMAN AND GOLDEN RATIO

ORGANISMS AND GOLDEN RATIO

Learn more about fractals and how we see and apply them in our world today at the Fractal Foundation.

Fractals are another intriguing mathematical shape that we seen in nature. A fractal is a self-similar, repeating shape, meaning the same basic shape is seen again and again in the shape itself. In other words, if you were to zoom way in or zoom way out, the same shape is seen throughout. Fractals make up many aspects of our world, included the leaves of ferns, tree branches, the branching of neurons in our brain, and coastlines.

Fractals in Nature

Another of nature’s geometric wonders is the hexagon. A regular hexagon has 6 sides of equal length, and this shape is seen again and again in the world around us. The most common example of nature using hexagons is in a bee hive. Bees build their hive using a tessellation of hexagons. But did you know that every snowflake is also in the shape of a hexagon? We also see hexagons in the bubbles that make up a raft bubble. Although we usually think of bubbles as round, when many bubbles get pushed together on the surface of water, they take the shape of hexagons.

Hexagons in Nature

They build the ends of the honeycombs by raising 13 degrees each. In this way, even if the comb stands upright, the honey does not flow out.

Bees visit flowers in many different regions every day and use a lot of energy. That's why they learn to fly on the best route to save energy and time. Bees use the hexagonal shape of their honeycombs to make full use of the unit area and make honeycombs with the least amount of material. In addition, the angle of the honeycomb pores made by all female honey bees is 70 degrees and 32 minutes.

Food-seeking bees regularly solve the problem of finding the shortest path as soon as possible.

BEES AND MATH

Parallel and Meridian in Nature

Proportion and Graphs in Nature

Concentric means the circles all share the same center, but have different radii. This means the circles are all different sizes, one inside the other. A common example is in the ripples of a pond when something hits the surface of the water. But we also see concentric circles in the layers of an onion and the rings of trees that form as it grows and ages. If you live near woods, you might go looking for a fallen tree to count the rings, or look for an orb spider web, which is built with nearly perfect concentric circles.

Concentric Circles in Nature

Moving away from planet earth, we can also see many of these same mathematical features in outer space. Because of math. The moon is approximately 400 times smaller than the sun, but it is also approximately 400 times further away. This symmetry allows for a total solar eclipse that doesn’t seem to happen on any other planet.

Math in Outer Space

Dragonfly wing

neurons

blood vessels

spider web

frozen glass

Isn’t nature amazing???

Let's watch!

Eslem-Büsra-BurcuSudenur-Elif-Minel

Luca-Emilia-Teodor-Natalia

Eda ACARfrom Sehit Emre Karaaslan VTAHS,Turkey

Elena Amalia COMANESCUfrom Scoala Gimnaziala ”Mircea cel Bătrân” Pitesti

From Our Students!

Count how many times a cricket chirps for 25 seconds. Divide this number by 3 and add 4 to the result. The value you get will give you an approximate value of the air temperature (°C)

There is a relationship between cricket sounds and air temperature!

The donkey is a good guide!

+ info

INTERESTING

It never forgets a road it takes and does not deviate from it. For this reason, they put a donkey that has gone this way before as a guide in front of camel or mule caravans.Anatolian villagers, who do not have any architectural knowledge, use their donkey to create a path in the mountains. They walk a donkey alone on a mountain without a path, and decide that the points he passes through are the most convenient way to pass. The villagers have known from experience that the animal can find the path that it can take with the least energy. Donkey does not go above 7% slope on the ramp,It determines the most suitable route.

During "V" shaped flight, each bird flaps its wings, creating an air stream that lifts the bird behind. In this way, a group of geese flying can increase their flight range by 70% by using the air flow created by each other's wing beat.The reason this method works is because they all go in the same direction.

Birds flying in a V shape!

What makes them mathematically interesting is that they know how to count numbers. Cicadas coexist and use prime numbers to avoid the risk of being easily preyed. Some species of these insects, which you can encounter in nature, emerge from the ground every 13 years, and some species every 17 years. The reason why they instinctively arrange their life cycles in accordance with prime numbers is that 13 and 17 are prime, and the situations of two separate groups of insects emerging at the same time are possible only once in 221 years, which is the common multiple of 13 and 17. So, prime numbers are directly linked to the survival of the cicadas.

A cicada we often remember for their laziness!

INTERESTING

Plants and Mathematics!

+ info

INTERESTING

Plants use special angles for their leaves to receive maximum sunlight. For this, he divides the 360 ​​degrees into two parts using the golden ratio number (1.618): Its wide angle is 222.5 degrees. (This number is also the number of days the planet Venus orbits the sun.) Its small angle is 137.5 degrees. (This number is also the inverse of the fine structure constant in physics with respect to multiplication.)

Tamar Friedmann, one of the leading researchers, said, “17. I find it extraordinary that a purely mathematical formula from the 19th century indicates a physical system discovered 300 years later. " said. This discovery was made while explaining a quantum mechanical technique known as the variation principle in a lecture on quantum mechanics. While comparing the values ​​they obtained in the classroom with classical calculations, a strange trend was noticed in the proportions. Help was sought from Friedmann to understand this trend, they soon realized it was the manifesto of the Wallis pi formula (first achieved using physics). “We weren't looking for Wallis's pi formula,” Hagen said. It came before us in a moment. " said. Wallis's formula has been proven many times since 1655, but it all came from the world of mathematics. Kevin Knudson, who made mathematical calculations in this study, said, “It is surprising and enjoyable that the Pi formula takes place in the hydrogen atom. This situation is almost like magic. " said. “Nature has kept this secret from us for 80 years,” Friedmann said. "I am very glad that we found this out."

It has been discovered that the formula of pi number exists in hydrogen atom!

INTERESTING

PART2

PART3

PART1

Let's try it too!

Büsra ea

Sudenur ea

Eslem ea

Eda ACARfrom Sehit Emre Karaaslan VTAHS,Turkey

Elena Amalia COMANESCUfrom Scoala Gimnaziala ”Mircea cel Bătrân” Pitesti

Natalia T

Teodor E

Emilia G

Luca T

Team's Backstage

REFERENCES

Move forward to play the game!

Thanks!

REFERENCES

Play Time!