Hatcher-Topology-of-Numbers · Problem 2.2.2

Continued Fractions

Mathematics — Algebraic Topology · continued-fractions-square-roots

Problem

(a) Compute the continued fractions for

\sqrt{5}

and

\sqrt{23}

. (b) Using the continued fraction for

\sqrt{5}

, find the first convergent which gives a rational approximation to

\sqrt{5}

accurate to four decimal places.