**The 6th meeting of the Islander Math Circles, Spring 2014**

**Facilitators**: Dr. Philip Yaskin

**Agenda**: Polygon Differencing

**Problem**

Put 4 integers on the corners of a square. At the midpoint of each side put the positive difference of the numbers at the corners. Connect the midpoints to form a new square. Repeat this process until it terminates. What do you notice? Do you think this happens no matter what numbers you put on the 4 corners? Repeat this process with a triangle. Now what do you think about your conjecture about the square? Repeat this process for an N-gon (a polygon with N sides). For which N’s does the process behave like a square? For which does it behave like the triangle? Prove your conjectures.

**Survey from National Association of Math Circles**