Topology of Numbers · Problem 2.1.1

Continued Fractions — Allen Hatcher

Mathematics — Number Theory · finite-continued-fractions

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).