Fibonacci Numbers: In Math

The Fibonacci numbers are of importance in nature. So many aspects of this mathematical series are found in nature, that it seems impossible it is mere coincidence.

The series is of decided important to both mathematicians and scientists as well. By way of simple definition, a sequence or series of Fibonacci numbers has its first two values, zero and one. Thereafter, the value of each number equals the sum of the previous two numbers.

Fibonacci Numbers: It All Boils Down

The sequence or series of numbers runs 0, 1, 1, 2, 3, 5, 8…, since 0 + 1 = 1, then 1 + 1 = 2, then 1 + 2 =3, then 2 + 3 = 5, and so on.

This can be expressed in equation form as

F_n = F_n-1 + F_n-2

Don’t see how this works? Consider an example. Take the value of n to be seven, i.e., n = 7. Then the equation becomes

F₇ = F₆ + F₅

Now F₆ is the sixth Fibonacci number. Counting them off, we see

• F₀ = 0
• F₁ = 1
• F₂ = 1
• F₃ = 2
• F₄ = 3
• F₅ = 5
• F₆ = 8

Then what is n = 7, which so far we have not listed or mentioned? Using our equation

F₇ = F₆ + F₅ = 8 + 5 = 13

The series is an “infinite series,” as the numbers never stop—we can continue increasing n, and hence, F_n, indefinitely.

We mentioned above that the Fibonacci series is important in nature. They are also beautiful in their manifestations therein. We will discuss that in

Fibonacci Numbers: In Nature

References:

• Museum of Mathematics: Fibonacci Numbers of Sunflower Seed Spirals

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