Steinhaus' Problem on Partition of a Hyperbolic Triangle

Year 2018, Volume: 9, 98 - 102, 28.12.2018

Oğuzhan Demirel

Abstract

Hugo Steinhaus ([1],[2]) has asked whether inside each acute triangle there is a point from which perpendiculars to the sides divide the triangle into three parts of equal areas. In this paper, we present a solution of this problem in the Poincaré disc model of hyperbolic geometry.

Keywords

Steinhaus' problem, hyperbolic triangle, hyperbolic quadrilateral, Gauss-Bonnet theorem

References

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