What do the chambers of a nautilus shell have in common with the Parthenon and playing cards? It turns out that their forms are examples of a standard proportion. It is called a "golden ratio" also know as a "Perfect Ratio"

There is a fundamental ratio found over and over again in nature that seems to please human perceptions. Geometrically, it can be defined as the ratio obtained if a line is divided so that the length of the shorter segment is in the same proportion to that of the longer segment as the length of the longer segment is to the entire line. Mathematically, these ratios are such that the longer segment is 1.618054 times the length of the shorter segment, while the shorter is 0.618054 times the longer.

These are remarkable numbers. Not only are the figures after the decimal point identical in both, but each is the reciprocal of the other (that is, the number 1 divided by either yields the other). These are the only two numbers that demonstrate this property. Unlike pi, another fundamental constant in which the decimals extend to infinity (3.14159. . .), these factors are exact after the first six decimals.

The earliest evidence of human appreciation for the pleasing qualities of these proportions is found in the pyramids at Giza, which appear to have been built with a 5 to 8 ratio between height and base. This is a close approximation (0.625) to the "perfect" ratio, although scholars disagree over whether the Egyptians were actually aware of it.

Even if it is not certain that the Egyptians knew of the ratio, there is no question that the Greeks had been able to calculate it. They called it the "golden ratio." Not understanding why, they knew that it felt good and it looked good, and they incorporated it into much of their art and into many of their buildings (including the Parthenon, which is generally considered to be antiquity's most perfect structure)

The secret was lost with the fall of Greece, but it began to resurface in the 16th century when Leonardo da Vinci utilized it in his painting and sculpture. Soon, many of the masters began to proportion their canvases according to the golden ratio, and it is still the shape most preferred today for anything from window blinds to table tops.

But it is not just the artistic eye that appreciates the golden ratio (or the artistic ear, for that matter--musical harmonics are also based on it). Its expression is found almost any place we look in nature.