Topology of Numbers · Problem 2.1.6

Continued Fractions — Allen Hatcher

Mathematics — Number Theory · continued-fractions-farey-diagram

Problem

Compute the strip of triangles corresponding to the continued fraction for

7/19

and compare this with the sequence of matrices reducing

\begin{pmatrix} 3 & 7 \\ 8 & 19 \end{pmatrix}

\begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}

by a sequence of operations subtracting one column from the other. (See the proof of Proposition 1.1.)