golden ratio (approx. 1.6180339887)

https://gyazo.com/7e5d2c3122176fd93f0b31a6aae558fd

Top: The golden ratio φ is obtained by taking the distance from the midpoint of the lower side of the square to the vertex on the lower extension.

Bottom: If isosceles triangle A with base 1 and isosceles φ is placed inside isosceles triangle B with base 1/φ and isosceles 1, which is similar to itself, the remaining part C becomes an isosceles triangle with base φ and isosceles 1. It follows from this that the magnitude of the interior angles of the triangle are 1:2:3. This triangle is similar to the triangle that appears when a pentagram is superimposed on a regular pentagon.

Middle: If a line segment is divided into φ:1:φ and its φ+1 part is further divided into φ:1:φ, the left endpoint of the earlier division coincides with the right endpoint of the later division. ((φ+1)/(2φ+1)*(φ+1)=φ) The algorithm that uses this feature is the golden partition search.

---