Have you ever wondered why index cards are 3x5, and photos are 4x6? Why are some things beautiful and some things feel slightly… off?
Well, we have the Golden Ratio to explain that. The Golden Ratio is a number (1.61803 to be exact) that explains a proportion that the human eye finds beautiful. Basically, we like the longer part of something to be a smidge over one-and-a-half-times longer than the shorter part.
Take for instance, these two green lines. The top line is one-and-a-half times as long as the bottom line, because six equals 4 plus half of 4. (6=4+2) These two lines follow the Golden Ratio. The two red lines are also following the Golden Ratio. Any two lines can follow the Golden Ratio, no matter how long they are, as long as they are the right length compared to each other. You can use these lines to build rectangles, like the 4x6 rectangles that are commonly used for photographs. You can also build much more complex shapes and objects.
The Golden Ratio is found in nature, too. Animals as diverse as dolphins and tigers, penguins and ants, all have features placed in relation to each other according to the Golden Ratio.
The Golden Ratio explains mathematically what we can already see. It comes in handy when someone is building a building (take the Parthenon in Athens) or painting a painting and they need to know beforehand what is going to look right and what would look weird.
Why do we like things that follow the Golden Ratio? That is a much harder question, one that many scientists and mathematicians debate. It is good to remember that the Golden Ratio is in itself an explanation; it does not create the beauty that we see, it simply explains and then predicts mathematically what we will find beautiful.