Steinhaus' Problem on Partition of a Hyperbolic Triangle

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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