The golden ratio in mathematics is the irrational number (1 + sqrt 5)/2. A decimal approximation of the number is 1.618. The German astronomer Johannes Kepler and his contemporaries were the first to call it the golden ratio.
The golden ratio's origin dates back to around 500 B.C. It is known for providing an aesthetically pleasing proportion for the sides of rectangles. The ancient Greeks were the first to observe the aesthetic qualities that result from using the golden ratio. The golden ratio was also influential in the work of Leonardo da Vinci and other Renaissance figures.
The golden ratio is relevant to modern mathematics, as it often occurs in descriptions of fractals, which are of particular importance to chaos theory.