The golden ratio has always had particular relevance in science and art thanks to its properties and appearance. Talking about math:
A golden rectangle can be split into two smaller golden rectangles (it maintains its proportions).
The golden ratio deeply correlates with the number 5. This number appears in its definition (φ = (1 + √5)/2) and the pentagon as the ratio between diagonal and side.
In arts, the golden ratio appeared more recently: Dalí, for example, used this ratio in many of its works. Read more