´Phi, commonly known as the Golden Ratio, is an irrational number with many fascinating properties. It can be derived with this equation:
(Image from Wikipedia)
I won’t delve into the various examples of phi which can be found in nature and art. There are many articles on the web concerning phi; a good starting point is the Wikipedia entry.
I will mention a visual and geometrical way to grasp this irrational number. Imagine a square, then imagine that the right-hand side of the square comes loose at the top-right corner and falls flat, continuing the bottom side of the square towards the right. Imagine a new side extending vertically and a connecting line extending from this new line’s top leftwards towards the terminus of the top of the square; what results is a rectangle. The ratio between the lengths of the long and short sides of this new rectangle is phi, the Golden Ratio.
A film-maker named Cristobal Vila has produced a very well-done video illustrating the Golden Ratio. Watch it, I’m certain you will enjoy it:
My friend Jeff called this video to my attention. Thanks, Jeff!