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

### 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.
3:30 PM
All are welcome!
Palenske 227
April 25, 2013