George Spahn, Rutgers University

Abstract

OEIS Sequence A359146 gives the number of different aspect ratios that are possible when partitioning a square into n similar rectangles. We will discuss several algorithms that have been used to compute the first few terms of this sequence and see a theoretical result that connects the problem to continued fractions. As a fun challenge to do before the talk, you can try to compute a(3), the number of different ratios that are possible when dividing up a square into 3 similar rectangles (not necessarily of the same size).

Link to video: https://vimeo.com/814661779

Presented Via Zoom: https://rutgers.zoom.us/j/94346444480

Password: 6564120420

For further information see: https://sites.math.rutgers.edu/~zeilberg/expmath/