It was formally discovered by the Greeks and incorporated into their art and architecture, but it has been shown to occur even in prehistoric art, possibly as a function of Man's natural affinity for it's beauty.
The rectangle at left has a vertical edge length of 1 the horizontal or width of the rectangle is 1.618
If we make a line inside and form a square (far left) it creates another 'golden rectangle' (at right) this subdivision continues inward in a spiral fashion tracing the form of a perfect PHI spiral seen in galaxies, seashells ....
Below LEFT is a fractal made of Phi sized circles in a symmetrical relationship
the Five Sided Pentagon has a huge variety of Golden Section Possibilities,
more Penrose Tile possibilities from the fractal page of Jos Leys
I printed out a few pages of tiles on heavy card-stock paper and here's my first arrangement
Another Perfect Phi Rectangle
Image Credit: Allan Brown - www.roundhillpress.com
Master Artist Paul Laffoley's Paintings (see gallery) often incorporate PHI on many levels
-More PHI in art and design
above: Icosa-dodeca phi-ratio recursive solid that most of the rant above is based on.