This seemingly magical result from Futility Closet defies proof at first. Go to the Wolfram demo by Jay Warendorff and then …

“Grab point B above and drag it to a new location. Surprisingly, M, the midpoint of RS, doesn’t move.

This works for any triangle — draw squares on two of its sides, note their common vertex, and draw a line that connects the vertices of the respective squares that lie opposite that point. Now changing the location of the common vertex does not change the location of the midpoint of the line.

It was discovered by Dutch mathematician Oene Bottema.”

As we shall see, Bottema’s Theorem has shown up in other guises as well.