This is the “golden ratio,”a.k.a. the “golden mean,”the “golden section,” and the “divine proportion.” It is a proportional relation obtained by dividing a line, or a plane figure, so that the shorter part is to the longer part as the longer part is to the whole. If you take a “golden rectangle” — one whose length-to-breadth is in the golden ratio — and snip out a square, what remains is another, smaller golden rectangle. What makes the golden ratio special to mathematicians is the number of properties it possesses. But what makes it extraordinary to the world is its relation to beauty. The golden ratio has been evoked through the ages to express perfection.

Examples abound. The Egyptians called it the “sacred ratio,” and applied it to the building of the pyramids.

The Greeks used it in the construction of the Parthenon. It is said that daVinci painted the face of the Mona Lisa to fit inside a golden rectangle. People like the architect Corbusier and the composer Bartók have consciously embodied it in their work. And daily in art and science classrooms students discover that geometric forms expressing the golden ratio are simply the most appealing to the eye.