Golden Ratio

Two quantities are said to be in the golden ratio when the ratio of the larger to the smaller equals the ratio of their sum to the larger, a relationship usually denoted by the Greek letter phi and equal to one plus the square root of five, divided by two, approximately 1.618. The earliest known mathematical definition of the ratio appears in Euclid's Elements, around 300 BC, which describes it as dividing a line into what Euclid called its extreme and mean ratio. The golden ratio is the limiting value approached by the ratio of consecutive terms of the Fibonacci sequence as the sequence grows, and, algebraically, phi is the positive root of the equation phi squared equals phi plus one.