Mathematical Trends in Nature — 1

There is a very interesting sequence of numbers, presented by the Italian mathematician Leonardo of Pisa (aka Fibonacci), called the Fibonacci sequence. The sequence goes like this –

1. Take 1 as the 1st term of the sequence

2. Take 1 as the 2nd term of the sequence too

3. For the 3rd term, add the 1st and the 2nd term. Thus, you get 1+1 = 2 as the 3rd term of this sequence

4. For the 4th term, add the 2nd and the 3rd term. This time, you get 1+2 =3 as the 4th term of the sequence

5. For the 5th term, add the 3rd and the 4th term of the sequence, and you will get 2+3 = 5 as that 5th term

6. Hence, in general, to find any term in this sequence, we just add up the last two terms of the sequence. For example, the 9th term of this sequence will be the sum of the 8th and the 7th term of the sequence. We can use this rule to find out all the terms of this sequence, except for the 1st and the 2nd term, which are both fixed at 1.

The resulting sequence is a rather beautiful one –

1, 1, 2, 3, 5, 8, 13, 21, 34, 55

Well what’s beautiful about it, it’s just a bunch of random numbers written next to each other?

Well let’s look at a few wonderful observations –

Fibo1
  1. Flower Petals — The number of flower petals in a flower very often corresponds to one of the numbers obtained in a Fibonacci sequence, i.e., 1, 1, 2, 3, 5, 8 etc. (called Fibonacci numbers)
Credit — British_Israel.us
Credit — British_Israel.us

2. Tree branches — The branches of a tree too follow a Fibonacci sequence in their growth cycles (assuming of course that greedy humans don’t interfere with their natural growth)

Fibo3

3. DNA Molecule — Even the length and width of a DNA molecule are 34 Å and 21 Å respectively

The Fibonacci Spiral -

Credit — Mathisfun

If you draw a sequence of quarter circles with the radius of each quarter circle equal to consecutive Fibonacci numbers, you end up with what is called a Fibonacci Spiral. This spiral is the form found in most of the naturally occurring spirals –

  1. Snail shells,

2. human anatomy,

3. and even hurricanes

Can you think of other ways in which the Fibonacci Sequence shows up in nature around us?

Can you explain why most naturally occurring spirals have the form of a Fibonacci Spiral?


Originally published at LetsMath.