Golden ratio

ratio between two quantities whose sum is at the same ratio to the larger one

drawing by Leonardo da Vinci

thumb|upright=1.2|Pentagram A pentagram (sometimes known as a pentalpha, pentangle, or star pentagon) is a regular five-pointed star polygon, formed from the diagonal line segments of a convex (or simple, or non-self-intersecting) regular pentagon. Drawing a circle around the five points creates a similar symbol referred to as the pentacle, which is used widely by Wiccans and in paganism, or as a sign of life and connections, but there is also a inverted version.

Rectangle with side lengths in the golden ratio

A right triangle whose edge lengths form a geometric progression

Catalan polyhedron

isosceles triangle in which the duplicated side is in the golden ratio to the distinct side

non-periodic tiling of the plane

Catalan polyhedron

plane curve

division of 360° angle into two sub-angles, such that one is 1.618034 times bigger than the other (i.e. the golden ratio or ɸ)

rhombus whose diagonal lengths are in the golden ratio

technique for finding the maximum of a unimodal function by probing a sequence of points whose distances decrease in the golden ratio at each step

unique real number solution to the equation x^3-x^2-1=0

sequence equivalent to its runs transform

geometrical shape

positional numeral system

English-American inventor and polymath (1871–1950)

self-similar geometric figure