Golden Ratio

The Golden Ratio is one of the first discovered irrational numbers. Because it is irrational, it cannot be expressed exactly as a fraction or integer. The definition of the golden ratio is below and can be used in bc:

(sqrt(5)+1)/2

Unlike Pi, it is a non-transcendental number because it uses a square root, which makes it easier to compute than pi despite it being "more irrational". The Golden Ratio is used in screen displays because most screens have an aspect ratio of 16.1x10 which is the golden ratio to 2 decimal places. Here are the first six digits after the decimal point:

1.618033

The Golden Ratio is used in the Fibonacci sequence and the powers of this number (also known as phi) get increasingly close to integers as the top number increases. The Golden Ratio is the only number that when squared, n+1 is the output.