Golden Ratio:

The golden ratio also is called the golden mean or golden section.Other names include extreme and mean ratio,medial section, divine proportion, divine section , golden proportion, golden cut,and golden number.Some twentieth-century artists and architects, including Le Corbusier and Dalí, have proportioned their works to approximate the golden ratio—especially in the form of the golden rectangle, in which the ratio of the longer side to the shorter is the golden ratio—believing this proportion to be aesthetically pleasing. The golden ratio appears in some patterns in nature, including the spiral arrangement of leaves and other plant parts.

Binary: 1.1001111000110111011...

Decimal: 1.6180339887498948482... OEIS A001622

Hexadecimal: 1.9E3779B97F4A7C15F39...

Continued fraction: 1+1/(1+1/(1+1/(1+1/(1+......))))