The Golden Ratio
The Golden Ratio, or The Divine Proportion, refers to the amount of space found between objects or the relationship between numbers. Found in nature, most clearly in the nautilus shell, the golden ratio applies in a multitude of contexts: art, math, design, and architecture and when followed makes those objects the most visually appealing.
The Greek philosopher Pythagoras discovered the concept of harmony when he began his studies of proportion while listening to the different sounds given off by stringed instruments and the different sounds they produced. In further studies of nature, he observed certain patterns and numbers reoccurring. Pythagoras believed that beauty was associated with this ratio of small integers, phi.
According to legend, Phidias (500 BC - 432 BC), a Greek sculptor and mathematician, studied phi and applied it to the design of sculptures for the Parthenon.
Fibonacci Sequences and the Golden Ratio
The Fibonacci sequence describes a mathematical pattern where, starting with 1, by adding the previous number, an exponential pattern of numbers occurs. 1+1 = 2; 1+2 = 3; 2+3 = 5; 5+8 = 13; 8+13 = 21, and on it goes. This was named after Leonardo Bonacci, an Italian mathematician from the 12th Century, however it also appeared in Sanskrit writings in India at about the same time.
Perhaps what is more interesting is to do with visual perception. Psychologist Adrian Bejan suggested in 2009 that the depth perception and field of vision of the human eye allows us to perceive, and therefore understand, stimuli that has the proportion of the golden ratio. Ever wondered why the popular iPad and iPhone displays are 3:2 and 5:8 ratios? This may be the reason why.