The Golden Mean

The Golden Mean The Golden Ratio
The Golden Mean ratio is 1 to 1.6

Some golden mean ratios:

• Legal size paper
• 11×17 is almost golden mean ratio
• Your outstretched hand (fingers together)
• The distance between the knuckles on your fingers
(the first knuckle is 1, the distance between the first and second is 1.6, etc.)
• The veins on most leaves
• Most Greek architecture is 1 part high to 1.6 parts wide
• Greek columns – the column is one part, the distance between the columns is 1.6
• Current window sizing

 

Here is a geometric connection. Starting with a single Golden rectangle (of length and width 1), there is a natural sequence of nested Golden rectangles obtained by removing the leftmost square from the first rectangle, the topmost square from the second rectangle, etc.

The Golden Mean within the Golden Mean

The length and width of the nth Golden rectangle can be written as linear expressions where the coefficients a and b are always Fibonacci numbers! These Golden rectangles can be inscribed in a logarithmic spiral as pictured.

Porttrait using the Golden Mean Here are basic Fibonacci number progressions:
The Fibonacci numbers are 0, 1, 1, 2, 3, 5, 8, 13, … (add the last two to get the next)
The Golden Section numbers are ±0·61803 39887… and ±1·61803 39887