Albion College

Mathematics and Computer Science

Mathematics and Computer Science

COLLOQUIUM

A Dialogue between Additive Functions and Squared Rectangles

Mingjia Yang, `13

Rectangles that can be partitioned into squares are called squared rectangles.
This talk will demonstrate and prove one surprising property of squared rectangles:
the ratio of width/length is rational!
Which means, if we have a rectangle of width $\sqrt{2}$ and length 0.8 (of the same unit),
then we know this rectangle cannot be squared! We will go over a proof of this result using
additive functions. The proof itself is almost as beautiful as the result,
since we see how different areas of mathematics interact with each other in a deep way.