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.