Maybe you hate the backsplash tiles behind your kitchen sink. I know I do. Not your tiles, I mean – mine. Their pattern is a boring grid; their color, a grubby off-white (if you’ve ever dug up grubs in your garden, you know what color I mean). A few of the tiles are stamped with chintzy brown sunflowers in a listless attempt at cheer. It probably doesn’t help that I hate our kitchen sink as well, a sink wedged in a countertop corner for added inconvenience.

But maybe you’re lucky. Maybe you have a convenient kitchen sink and exciting backsplash tile. If your backsplash tile is laid in a hopscotch pattern, you even have the Pythagorean theorem lurking right behind your sink. To the left is a backsplash much nicer than mine, tastefully tiled in a hopscotch pattern (well, tasteful aside from the peculiar choice of blue grout). To mathematicians, the hopscotch pattern is known as “Pythagorean tiling”, because of how beautifully it illustrates the Pythagorean theorem. Several proofs of the Pythagorean theorem exist, some of which are more intuitive than others. To me, the diagram superimposed on the hopscotch tiling produces one of the most intuitive proofs, especially for children. If you like, you can knock off reading right now and do the proof yourself: the diagram has all the labeling you need.