In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. A ratio is a fraction. The fraction ¾ expresses a ratio, 3 out of 4, or 3 is to 4.

Below, the order of the fractions is expressed by placing them on opposite sides of the equal sign as opposed to the graphic above (graphic below is better).

Below, the order of the fractions is expressed by placing them on opposite sides of the equal sign as opposed to the graphic above (graphic below is better).

φ

The golden ratio, symbolized by the Greek letter

The golden ratio, symbolized by the Greek letter

*phi*as shown above*,*is a special number approximately equal to 1.618. It appears many times in geometry, art, and architecture. Opposite is the Parthenon. The number even shows up in describing the perfectly proportioned human body and face.