Fibonacci Sequence

One of the most famous recursive sequences is the Fibonacci Sequence. The next term in the Fibonacci Sequence is the sum of the previous two terms, with the first two terms being 1. Expressed mathematically the sequence is:
Fib equation 1.png

Finding the first several terms of the Fibonacci Sequence finds them to be:

Fib sequence.png

The Fibonacci Sequence is found in nature, specifically the golden curve. To create the golden curve, you, take a square whose lengths are equivalent to its associated number in the sequence. So, the first term is one, and thus a square with a side of one is:

Fib curve - 2.png

With the next term also being 1, adding a second square of length one on top of the first one:

Fib curve - 3.png

a3 is 2, and adding a square of length 2 to the right of the other squares:

Fib curve - 4.png

We can continue this same process, adding squares whose measures are the values in the Fibonacci Sequence we get the following squares:

Fib curve - 6.png

To add the golden curve to these squares, you draw a curve that goes through the opposite corners of the drawn squares. As shown below:

Fib curve - 1.png