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Experimental Mathematics Seminar

Partitioning a Square into Similar Rectangles

George Spahn, Rutgers University

Location:  Zoom
Date & time: Thursday, 30 March 2023 at 5:00PM - 6:00PM

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).

Zoom Link
[password: The 20th Catalan number, alias (40)!/(20!*21!), alias 6564120420 ]