Department of

September 2018October 2018 November 2018 Su Mo Tu WeThFr Sa Su Mo Tu We Th Fr Sa Su Mo Tu We Th Fr Sa 1 1 2 3 4 5 6 1 2 3 2 3 4 5 6 7 8 7 8 9 10 11 12 13 4 5 6 7 8 9 10 9 10 11 12 13 14 15 14 15 16 17 18 19 20 11 12 13 14 15 16 17 16 17 18 192021 22 21 22 23 24 25 26 27 18 19 20 21 22 23 24 23 24 25 26 27 28 29 28 29 30 31 25 26 27 28 29 30 30

Wednesday, October 3, 2018

**Abstract:** Continued fractions are frequently studied in number theory, but they can also be described geometrically. I will talk about continued fraction expansions as dynamical systems, and connect this symbolic system to tessellations. The first part will focus on the "regular" or "simple" continued fractions, where all of the numerators are 1. Then, I will show what happens when all of the numerators are $\pm 1$ and the denominators are all even or all odd.