I have a go-to math fact to bring out at parties when people are want to hear one. The cute part is that they can do it themselves.

Take a pen and paper and draw a quadrilateral. There are no restrictions (it can be concave or self-intersecting), but don’t make it too close to the sides of the paper. Now, for each edge, draw the square containing that edge that is outside the quadrilateral. Put a dot in the center of each of the four squares, and draw a line connecting opposite dots, ie, those that came from opposite edges.

The Punchline: The lines you just drew are the same length, and perpendicular.

I wrote it up and drew up a pictoral proof on my (mostly-defunct) blog sometime ago.

I have a go-to math fact to bring out at parties when people want to hear one. The cute part is that they can do it themselves.

Take a pen and paper and draw a quadrilateral. There are no restrictions (it can be concave or self-intersecting), but don’t make it too close to the sides of the paper. Now, for each edge, draw the square containing that edge that is outside the quadrilateral. Put a dot in the center of each of the four squares, and draw a line connecting opposite dots, ie, those that came from opposite edges.

The Punchline: The lines you just drew are the same length, and perpendicular.

I wrote it up and drew up a pictoral proof on my (mostly-defunct) blog sometime ago.