**Application of Mathematics In Nature**

**By Samiya Arora**

Symmetry

Symmetry places a great role in nature – in occurs in many plants, animals, fruits, etc. There are 2 types of symmetry in nature; reflective and rotational symmetry. Rotational symmetry occurs when a rotational pattern occurs around a centre point, and each spiral or pattern is the same as the one before; just like a spider web. This type of symmetry often occurs in plants. An example of rotational symmetry is starfish.

Symmetry

Radial Symmetry

Radial symmetry is found is many fruits and plants such as oranges, apples, kiwi, butterflies Dahlia and snowflakes. When a straight line is cut through the centre point of any object, producing two identical parts, it is known as radial symmetry. For example, take an orange; if a straight line is cut through from the tip to the bottom in the centre, you will have 2 identical pieces.

The Golden Rectangle

Fibonacci Numbers

Fibonacci numbers play the most important role of all, in terms of ‘application of math in nature.’ First, let’s start with Fibonacci numbers. What are they? Fibonacci numbers are a sequence of numbers starting from 1, in which the previous two numbers are added to give the next number –

0 + 1 = 1

1 + 1 = 2 5+8=13

2 + 1 = 3 8+13=21

2 + 3 = 5 13+21=34.....................

3 + 5 = 8

This gives us the pattern of 1, 1, 2, 3, 5 ,8, 13, 21, 34 ………and so on.

This pattern applies everywhere in nature; a flower can only have the number of petals of a Fibonacci number. This is because the first two petals make the next one, then then the previous two petals make the next one, and so on. This is why a 4- leaved clover is so hard to find.

Now to create the golden spiral: a line must be drawn through every box, in a spiral like pattern, like so.

Golden Spiral

Now you must be wondering, what is so important about the golden spiral, right? Well, the golden spiral can actually be found in everything around us - faces, flowers, many ancient buildings, solar systems, clouds, tsunamis, waves, nautilus shells, eggs, Romanesco broccoli, monarch caterpillars, American giant millipede, animals, the ‘Mona Lisa’ – the list is endless.

What's So Special About It?

Now comes the ‘Golden Ratio’. The Golden Ratio is the division of a quantity into 2 unequal parts, in which the bigger part over the smaller part is equal to the whole quantity over the larger part.

Here, a line is divided into 2 unequal proportions, by the figure of ‘C’, and put into proportions of the ‘Golden Ratio’. (Note – the measurements must be exact)

AB /AC = AC / BC

A B C

______________________________________

8 / 5 = 1.6

13 / 8 = 1.625….. 1.618033…….

21 / 13 = 1.615……. ..

34 / 21 = 1.619…….

55 / 34 = 1.617…….

89 / 55 = 1.61818…..

= 1. 6180339…………..

Also known as Phi, an ancient Greek symbol:

Now again the question arises, why is this number so important? Well, the ‘Golden Ratio’ has been used to build many, many ancient buildings, such as the Parthenon (an ancient Greek building), and it is used in everyday art, architecture and design.

Here is an example of AC / AB = AC / AB

As you can see, the height of the temple (A) refers to the height of the lower part (B), in the same way the height of the lower part refers to the height of the upper part, also in the same way as the width of the temple (D) refers to the width of all the pillars (E).

A

C

B

D

E

A German researcher measured more than 2000 bodies, and concluded that it is the manifestation of a medium statistical, which is the division of the human body by the navel point. As you can see, the height of the human body (A) refers to the height of the lower part (B), in the same way as the lower part refers to the height of the upper part (C). The researcher found out that the proportions of a male body is 13/ 8, which equals 1.625, very close to the golden ratio.

C

B

A

Bibliography

http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibnat.html

http://www.botanical-online.com/english/plant_symmetry.htm

https://www.teachervision.com/math/resource/5990.html

http://www.inspirationgreen.com/fibonacci-sequence-in-nature

Arthur Benjamin: The magic of Fibonacci numbers

Gods Fingerprint→ The Fibonacci Sequence - Golden Ratio and The Fractal Nature of Reality

The absurd golden ratio | Robb Enzmann | TEDxMiamiUniversity

What is Golden Ratio - easy explanation

The End...

Thanks For Watching!

Here is the ‘Golden Rectangle’. As you can see, 2 boxes measured 1 x 1 have been situated vertically, with a square with a perimetre of 2 x 2 on its left. Next, a 3 x 3 box underneath it, 5 x 5 on its right, 8 x 8 above, 13 x 13 to the left, and the pattern continues. These Fibonacci measurements make up the perfect ‘Golden Rectangle’, which can be as large as infinity.

Application In Nature