##### Department of Mathematics,

University of California San Diego

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### Food For Thought Seminar

## Alex Eustis

#### UCSD

## A Weighted Tiling Model for Continued Fractions

##### Abstract:

Ever been curious about continued fractions? This talk will cover the basics, and demonstrate how they are closely related to weighted square-and-domino tilings. In particular we'll do a neat bijection that "compresses" a board with periodic weights into a smaller period-1 board, and then show how this can be used to calculate periodic continued fractions. In addition, one can prove a number of Fibonacci/Lucas identities combinatorially using this model.

### January 22, 2009

### 10:00 AM

### AP&M 7321

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