What is the golden ratio?
The golden ratio, also known as the golden number, golden proportion, or the divine proportion, is a ratio between two numbers that equals approximately 1.618. Usually written as the Greek letter phi, it is strongly associated with the Fibonacci sequence, a series of numbers wherein each number is added to the last. The Fibonacci numbers are 0, 1, 1, 2, 3, 5, 8, 13, 21, and so on, with the ratio of each number and the previous number gradually approaching 1.618, or phi.
History of the golden ratio.
The first known mention of the golden ratio is from around 300 BCE in Euclid’s Elements, the Classical Greek work on mathematics and geometry. Euclid and other early mathematicians like Pythagoras recognized the proportion, but they didn’t call it the golden ratio. It wasn’t until much later that the proportion would take on its mystique. In 1509, Italian mathematician Luca Pacioli published the book De divina proportione, which, alongside illustrations by Leonardo da Vinci, praised the ratio as representing divinely inspired simplicity and orderliness.
Because of Pacioli’s book and Leonardo’s illustrations, the golden ratio gained fame among mathematicians and artists. In the centuries since Pacioli’s book, many enthusiasts have claimed that the number is naturally pleasing to the eye, that it is a mathematical distillation of beauty, and that golden ratio line segments, golden rectangle side lengths, and golden triangles are represented throughout art history.