In mathematics, the Fibonacci numbers or Fibonacci sequence are the numbers in the following integer sequence. By definition, the first two numbers in the Fibonacci sequence are either 1 and 1, or 0 and 1, depending on the chosen starting point of the sequence, and each subsequent number is the sum of the previous two. In mathematical terms, the sequence *Fn* of Fibonacci numbers is defined by the recurrence relation.

The Fibonacci sequence is named after Italian mathematician Fibonacci. His 1202 book *Liber Abaci* introduced the sequence to Western European mathematics, although the sequence had been described earlier in Indian mathematics. By modern convention, the sequence begins either with *F*0 = 0 or with *F*1 = 1. The *Liber Abaci* began the sequence with *F*1 = 1.

Fibonacci numbers are closely related to Lucas numbers in that they are a complementary pair of Lucas sequences. They are intimately connected with the golden ratio; for example, the closest rational approximations to the ratio are 2/1, 3/2, 5/3, 8/5, … . Applications include computer algorithms such as the Fibonacci search technique and the Fibonacci heap data structure, and graphs called Fibonacci cubes used for interconnecting parallel and distributed systems. They also appear in biological settings, such as branching in trees, phyllotaxis (the arrangement of leaves on a stem), the fruit sprouts of a pineapple, the flowering of an artichoke, an uncurling fern and the arrangement of a pine cone‘s bracts.

Sacred Geometry and The Fibonacci Sequence have been subjects that I have been learning more and more about over the past few years and the more I learn the more in-tune with the rules of nature.

Artists and architects have been using geometrical and mathematical properties since ancient times. We’ve seen it used by architects from Ancient Egypt, Greece, and Rome, and by Renaissance artists like Michelangelo and Da Vinci. However, this animator wanted to showcase how these properties are used in nature … and he did so with mesmerizing results.

## Basic Fibonacci Sequence

The Fibonacci Sequence is the series of numbers:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, …

The next number is found by adding up the two numbers before it.

- The 2 is found by adding the two numbers before it (1+1)
- Similarly, the 3 is found by adding the two numbers before it (1+2),
- And the 5 is (2+3),
- and so on!

Example: the next number in the sequence above is 21+34 = **55**

It is that simple!

Here is a longer list:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610, 987, 1597, 2584, 4181, 6765, 10946, 17711, 28657, 46368, 75025, 121393, 196418, 317811, …

Can you figure out the next few numbers?