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Fuchsian group

{title2=$\Delta(p,q,r)$}
{wiki=Triangle_group}

When $1/p+1/q+1/r<1$, the orientation-preserving hyperbolic triangle group has presentation
$$
\Delta(p,q,r)=\langle a,b,c\mid a^p=b^q=c^r=abc=1\rangle
$$
and is a non-elementary Fuchsian group.

Hyperbolic triangle group

Past exam of the mathematics course of the University of Cambridge / 2026 / iii / Paper 133 / 3 / b / Solution

Hyperbolic triangle group ( $Δ (p, q, r)$ )

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Hyperbolic triangle group (Δ(p,q,r))

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Hyperbolic triangle group ( $Δ (p, q, r)$ )

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