One of the earliest principles that photographers learn is the Rule of Thirds. For a layperson it suffices to know that photographs appear much more pleasing to the eye when subjects are placed about a third of the way off-center, rather than being bang in the middle of the frame. But to the interested amateur or aspiring professional, it helps to know the mathematical principle behind this rule.
Artist of the Renaissance period realized the aesthetic qualities of the Golden Ratio and used it in their works. But its mathematical aspects have been studied by intellectuals since at least 2,400 years. Euclid, and before him, Pythagoras studied the golden ratio due to its frequent application in the geometry of lines, regular pentagrams and pentagons. It saw a resurgence in artistic, scientific and architectural circles since Luca Pacioli authored Divine Proportione in 1509.
Uma poses in her self-knit pink beanie cap in this rather benign application of the Golden Ratio.