/sci/ - Science & Math

This is how I make sense of the Pythagorean theorem, and I think it's the most intuitive. If you have tiles of any two different sizes, you can tile a space with them like in pic related. Then if you connect recurring points, you get a new grid of squares larger than the tiles you started with and tilted at an angle. No matter what recurring point you pick (could be the centers of the smaller squares, could be the centers of the larger squares, for example); when you connect them and make a grid, the pieces inside the grid can always be rearranged to make the one of each of the original tiles. This just makes sense. Then when you pick a corner for the recurring point, you form a right triangle with the tiles as the legs and the grid square as the hypotenuse.