Avish Dumir

Absolute Differences

Started May 19, 2023

Abstract or project description

Imagine labelling a polygon with integers on each side. Now, inscribe another polygon with the same number of sides, where each new side has the absolute difference of the numbers on the sides it touches. Repeat this process until some stable behaviour is exhibited (which, we believe, always happens). How long does this process take before convergence? What shapes go to all 0s and what shapes repeat some pattern? This number theory problem has many branches to explore! Using Python to help calculate differences of larger polygons. Some of the results suggest that polygons with 2^n+1 sides always converge to zero, this has not been confirmed.