Golden Rectangle

The Golden Rectangle, alleged to be the most aesthetically pleasing rectangular shape possible, was first constructed by Pythagoras in the 6th century BCE. It is defined as the rectangle which, when squared, leaves another golden rectangle behind. How does this work? Let's take a closer look at the rectangle itself.

The rectangle shown here is a Golden Rectangle with proportions x/y. The section labelled "a" is a square drawn in the rectangle with proportions x/x. The section labelled "b" is another Golden Rectangle, this one with proportions (y-x)/x. In other words, the ratio of the lengths of the sides of section "b" is the same as the ratio of the length of the sides of the entire large rectangle. This is the characteristic of a Golden Rectangle. When you square it (inscribe a square with lengths the same as the length of the short side of the rectangle), you are left with another rectangle with the same proportions as the original.