Los Angeles Math Circle

10/4 -- Group B: Continued fractions, part I (Prof. Christoph Thiele)

We will discuss the continued fraction expansion and talk a little bit about the golden ratio and its occurrence in arts and nature. Then we will calculate the continued fraction expansion of roots of small integers and discover some interesting structure in these expansions. This will lead to the understanding of a beautiful theorem named after Fermat but proven by Euler, that characterizes the primes that can be written as the sum of two squares.