Math Circles Meeting: May 10th, 2014

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

Facilitators: Dr. Philip Yaskin

Agenda: Polygon Differencing


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