As a huge math nerd and art hobbyist (especially photography), I get really excited when the two overlap. Have you ever heard of the Fibonacci sequence? It starts with 0, 1, then continues with each term equaling the sum of the previous two:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, etc.
What’s fascinating about the Fibonacci sequence is that it appears everywhere in nature in the form of the golden ratio. Dividing a number in the sequence by the preceding number approximates the golden ratio (the approximation becomes more accurate the further down the sequence the numbers are and approaches ~1.618). This ratio is expressed in the dimensions of conch shell spirals, the arrangement of branches on trees, the formation of petals on flowers, and even in proportions of the human body.
The golden ratio is used in art because shapes which express the ratio are more appealing to the eye–more beautiful. In photography, a common composition technique is the “rule-of-thirds” in which the subject or horizon line is placed a third of the way from the frame. This makes more interesting photographs than if the subject were in the center, and it works because it was derived from the golden ratio.
I think it’s incredible that this simple mathematical pattern seems to govern nature and even how we perceive beauty!