The Golden Rectangle

A rectangle with sides in the golden ratio (about 1.618:1) has a special property: cut off a square, and the leftover rectangle has the exact same proportions. You can repeat that cut forever. This self-similar quality is often called visually pleasing, and the proportion shows up in plenty of modern design layouts. It is also famously claimed for the Parthenon, though historians dispute that — there is no evidence the ancient Greeks used it, and the idea only dates to the 1850s.

Standard paper sizes (A4, Letter) are not quite golden, but they're designed with their own clever ratio. A-series paper uses a 1:√2 ratio so that folding a sheet in half produces a smaller sheet with identical proportions.