Hatcher-Topology-of-Numbers · Problem 2.1.1

Continued Fractions

Mathematics — Algebraic Topology · continued-fractions-computation

Problem

(a) Compute the values of the continued fractions

\frac{1}{1 + \frac{1}{3 + \frac{1}{5 + \frac{1}{7}}}}

and

\frac{1}{1 + \frac{1}{1 + \frac{1}{1 + \frac{1}{1 + \frac{1}{1 + \frac{1}{2}}}}}}}}

. (b) Compute the continued fraction expansions of

19/44

and

101/1020

. (c) Draw the strips of triangles corresponding to the continued fractions in parts (a) and (b).