NUMBERS (Discovery Channel)
The Universe's Greatest Mathematical Constants: No Holds Barred!
Math Joke of the Day

Have you heard the one about the statistician?

Probably...

return to the constant
return to the battlefield

Appearances in Art

A Nice Balance

face

The golden ratio appears in all kinds of paintings, sculptures, and architecture. Whether this frequency is by coincidence or not is up for debate. The Greeks believed that the golden ratio makes for some very pleasing shapes; it’s a nice balance between symmetry and asymmetry.

The Golden Rectangle

The ratio, when applied to the dimensions of a rectangle, creates a so called golden rectange that is very regular and pleasing to the eye. Even so, studies have shown that people have no significant preference for the golden rectangles over thinner or fatter ones.

another face

The Perfect Face

The golden ratio is also close to ratios in the human face, and it is thought that the perfect face would contain the golden ratio exactly. In 1509, Leonardo Da Vinci did the illustrations for Luca Pacioli’s Divina Proportione which explored the math behind the golden ratio and its uses in architecture and art. There is suspicion that Da Vinci went on to apply the golden ratio to his painting of the Mona Lisa.

(Face image based on woodcut from Luca Pacioli’s "Divina Proportione")