Mathematics in Nature

                       Mathematics in Nature

Mathematics is omnipresent. What we have in mathematics is the part of nature or the nature has helped human to learn mathematics. God has made everything in the world; whether it is a plant, the human, the Sun, the moon, the mountains, the rivers or any other things. Can you see the mathematics in all these things? Some of you might be excited to know mathematics can be seen or felt everywhere.

Have you ever thrown a pebble into the stagnant water or in river? What is the shape of the waves? It is circular.

The pupil of our eye is also circular. The equation of circle is x² + y² = r²

                                                                               

The light travels in a straight line. Let us do an experiment to prove this result.

Place two boards equal in shapes and identical holes on a table. Now focus the torch through one of the hole and you will find that the light comes out through another hole.

The equation of straight line is y = mx + c

Some of you might have visited the Nehru Planetarium. Those who have visited there must have seen that the planet move in an elliptical path.

                                                   The Solar System

 The equation of ellipse is

                                   
x² + y²     =1
a²      b²

                                                                                                                                         

When a batsman hits a ball for six it goes up in the air before hitting the ground. Can you name the shape the ball forms? It is a parabolic path. The equation of the Parabola is         y² = 4ax or x² = 4ay.

You can see the shape of Parabola during Diwali when fire is lit into the crackers. The parabolic shape can be found in the water fountain.

 

                           

                                                                                          

It is rightly said the Nature helps the men to learn Mathematics. You can see the different geometrical shapes in the Natural world besides that Nature forms different mathematical series. Some tree is in the shape of a triangle.

This shape is called the spiral. This spiral is called Archimedes Spiral. It was first discovered by Archimedes. The space between each line of the spiral and the one before and after is the same. The polar equation of this spiral is r = aө.  This spiral was first studied by Archimedes in 225 BC.  The inner structure of a sea shell also looks like a spiral.                                                                                 This spiral is called equiangular or logarithmic spiral. The curve of the spiral always intersects the outreaching radii at a fixed angle. Logarithmic spiral also occur in the curve of elephants’ tusk, the horns of wild sheep and even in canaries’ claws. The name equiangular spiral was given by Rene Descartes.

 Jacob Bernoulli (1654-1705) was so much fascinated by the properties of the logarithmic spiral that he had requested that it be carved on his tombstone with the Latin inscription Eadem Mutata Resurgo which means I shall arise the same though changed.

                                               

                                                                Inner shape of sea shell

Symmetry can be noticed everywhere in the Nature. There are different kinds of symmetry but most common of them which is found in the nature is called Bilateral symmetry. If you divide such symmetrical figure vertically in the middle then both the halves will be identical.

        

                             

                                 Butterfly                                                                                          

         Leaf showing symmetry


Crystals have rotational symmetries that may be twofold, threefold, fourfold, and six fold but not fivefold. 

Hexagonal Structure

                                                                                                       

 

Cubic Structure                                                                                                                           

Different geometrical shapes can be found in the fruits, vegetables and plants in the nature.        Apple when cut through middle a five point star can always be seen.

                       

Oranges where as look like sphere but when cut through middle the shape of triangles can be visible.

The cross section of bamboo is hexagonal in shape.

                                                                         

Trees planted at the two sides of road represent a parallel line. The two banks of the rivers also exhibit the example of parallel line.

Besides that there are many more shapes in nature and now it is for readers to find out the different other shapes in nature.

 During rain you must have noticed lightning of clouds. Can you remember its shape? It forms branches.

The most important thing in the nature is the presence of Fibonacci Numbers. 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 253, 377…are the Fibonacci numbers.

Here is the list of flowers whose petals form a Fibonacci sequence:-

Name of the flowers	Number of Petals
Iris , Lily	3
Wild Rose, Columbine	5
Delphium	8
Corn marigold, Cineraria	13
Chicory	21

 The above table shows the number of petals of these flowers form a Fibonacci sequence. Pine apples and pine cones spiral in anticlockwise and clockwise follow Fibonacci number pattern. The number of petals or spirals on seed head of sunflowers or cone flowers is mostly Fibonacci numbers.

The diagram above reveals the double spiraling of the daisy head. The daisy’s spiral ratio of 21:34 corresponds to two adjacent Fibonacci number. Besides that Fibonacci numbers can be visualized in fruits like banana, apple, pinecones etc. Banana has three sections; an apple has five sections where as in a pine cone there are 8 spirals in clockwise direction and 13 in anticlockwise direction    

                                                                       

                                                

 Banana (3)                 







Apple(5)  









          Pinecones (8 and 13)

The journey of Fibonacci numbers in nature does not stop here. Many vegetables also exhibit the pattern of Fibonacci numbers. Here is an interesting problem taken from Liber Abaci a famous book written by Leonardo of Pisa better known as Fibonacci in 1202AD. Fibonacci posed the following problem dealing with the number of offspring generated by a pair of rabbits conjured up in the imagination:

A man put one pair of rabbits in a certain place entirely summoned by a wall. How many pairs of rabbits can be produced from that pair in a year if the nature of these rabbits is such that every month each pair bears a new pair which from the second month on becomes productive?

Assuming that none of the rabbits dies; then the number of rabbits born will follow Fibonacci series.

Months	Adult Pairs	Young Pairs	Total
1	1	1	2
1	2	1	3
3	3	2	5
4	5	3	8
5	8	5	13
6	13	8	21
7	21	13	34
8	34	21	55
9	55	34	89

The images used here have been taken from different webpages which I came across while writing this article. I am thankful to all of them. 

Please don't forget to send your reaction to 

Rajesh Kumar Thakur

rkthakur1974@gmail.com