# Alhazen’s hyperbolic billiard problem

@article{Poirier2012AlhazensHB, title={Alhazen’s hyperbolic billiard problem}, author={Nathan Poirier and Michael Mcdaniel}, journal={Involve, A Journal of Mathematics}, year={2012}, volume={5}, pages={273-282} }

Given two points inside a circle in the hyperbolic plane, we study the problem of finding an isosceles triangle inscribed in the circle so that the two points belong to distinct congruent sides. By means of a reduction to the corresponding result in Euclidean geometry, we prove that this problem cannot generally be solved with hyperbolic ruler and compass. In his treatise on optics, written in Arabic, the scientist and mathematician Abu Ali al-H . asan ibn al-Haytham (965‐1039) posed the…

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