A Dialogue between Additive Functions and Squared Rectangles
Mingjia Yang, `13
Mathematics Major
Mathematics and Computer Science
Albion College
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.