cornergame

The Corner Game

Choose any four numbers and put them on the vertices of a square. Now make a new square by taking the absolute values of the differences of numbers on the original square to label the vertices of the new square.

For example, say you start with the labels 2, 5, 3, and 7 on the corners of your square like this.

2   5

7   3

Your next square would then be

3   2

4   5

where you place the differences in order as you take them around the first square (remember to take the positive differences). It does not matter what vertex you start with each time.

Now continue to make new squares in succession until you reach "the end". Try some different starting numbers. Amazing, huh? Prove that this always happens. What about polygons with a different number of sides? Try the triangle (1,1,0). Try 5, 6, and 7 sides, then try 8. Pretty amazing, huh?

Click here for Maple code to play the corner game.