Convergence of integer continued fractions: A geometric approach.

Mairi Walker (The Open University)

Frank Adams Room 1, Alan Turing Building,

It is well known that every simple continued fraction converges, but the same is not true for general integer continued fractions. In this talk we look at the problem of characterising convergent integer continued fractions, reformulating it into the problem of characterising closed paths in the Farey graph, an infinite tessellation of the upper half-plane by (ideal) hyperbolic triangles. We present an idea for solving this problem.

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