Continued Fractions, Geometry, and Dynamics

Event time: 
Tuesday, January 28, 2020 - 6:00pm
LOM 206
Paul Apisa
Speaker affiliation: 
Yale University
Event description: 

Why is 22/7 such a good approximation to pi? What does the space of invertible 2x2 matrices look like? What about the space of lattices in the plane? We will answer all these questions and connect the answers by introducing an elegant geometric way to think about continued fractions. As a bonus, along the way we’ll happen to meet a short, intuitive, geometric proof of the polar decomposition from linear algebra.