# Golden rectangle

A golden rectangle is a rectangle whose length to width ratio equal to the golden ratio, φ, which has a value of or approximately 1.618, assuming the length is the larger value. The following diagram shows what it looks like visually:

Golden rectangles have been used throughout history in architecture, art, and other areas, both intentionally or on accident, but there isn't a concensus on why this is. One of the proposed reasons for this is that shapes that adhere to the golden ratio are aesthetically pleasing.

Another potential reason is a special property of golden rectangles: if a rectangle is a golden rectangle, any new rectangle created by adding or removing a square from the golden rectangle, will also be a golden rectangle:

In the figure above, rectangle Z, with width b and length a, is a golden rectangle. Due to the property stated above, this means that the rectangle with width, a, and length, (a + b), is also a golden rectangle. If we were to have removed a square with dimensions b × b from rectangle Z, the remaining rectangle, Y, with dimensions c × b, would also be a golden rectangle:

Based on this property, it's possible to make numerous rectangles of varying sizes that are related by the golden ratio, which could be why some people see golden rectangles as aesthetically pleasing, on top of being easy to create patterns with.