The Golden Ratio Part 1 – Fibonacci

The golden ratio can be found in art, architecture, nature and mathematics. Let’s take a look at the Fibonacci sequence.

Golden Spiral
The golden rectangle is approximated by the Fibonacci numbers. The spiral embedded within the rectangle also approximates the golden spiral.

The Fibonacci sequence, formulated by Leonardo of Pisa also known as Fibonacci, is defined by starting with the numbers 0 and 1. New numbers are formed by adding the previous two numbers together. Thus: 0, 1, 1, 2, 3, 5, 8, 13, 21…

When the Fibonacci sequence is represented geometrically it forms an approximation of the golden rectangle. The golden spiral can approximated by tracing the corners. This spiral can be seen in the shapes of spiral galaxies.

Also each Fibonacci number, when divided by a previous number, gets closer and closer to the golden ratio. For example 8/5 = 1.6, 13/8 = 1.625, and 21/13 = 1.615 … and so on.

Thus the Fibonacci sequence embodies both the aesthetic and mathematical beauty of the golden ratio.