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Journals / Turkish Journal of Mathematics and Computer Science / 2018 / Cilt: 9

Steinhaus' Problem on Partition of a Hyperbolic Triangle

Oğuzhan DEMİREL
Pages
98–102
Publication Date
2018-12-28
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

In this paper, we present a solution of this problem in the Poincaré disc model of hyperbolic geometry.

📌 3 Key Takeaways

🎯
Objective & Hypothesis: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.
📊
Key Findings & Data: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.
💡
Conclusion & Impact:In this paper, we present a solution of this problem in the Poincaré disc model of hyperbolic geometry.
🔬Design:Modeling & Simulation
📍Scope:Comprehensive Sample
⚙️Variables:Steinhaus' problem · hyperbolic triangle · hyperbolic quadrilateral

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.

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Cite This Article

DEMİREL, O. (2018). Steinhaus' Problem on Partition of a Hyperbolic Triangle. Turkish Journal of Mathematics and Computer Science, Cilt: 9, 98–102. https://ajindex.com/articles/705422

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References (6)

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  2. Beardon, A.F., The Geometry of Discrete Groups, vol. 91 of Graduate Texts in Mathematics, Springer, New York, NY, USA, 1983.
  3. Ehrmann, J.P., Constructive solution of a generalization of Steinhaus’ problem on partition of a triangle, Forum Geom., 7(2007), 187–190.
  4. Ehrmann, J.P., On an affine variant of a Steinhaus’ problem, Forum Geom., 8(2008), 1–5.
  5. Steinhaus, H., Problem No. 132 (in Polish), Roczniki Polskiego Towarzystwa Matematycznego (Annales Societatis Mathematicae Polonae), Seria II, Wiadomosci Matematyczne, 9(1966), 99. Steinhaus, H., Problem No. 779 (in Polish), Matematyka, 19(1966), 92. Tyszka, A., Steinhaus’ problem cannot be solved with ruler and compass alone (in Polish), Matematyka, 49(1996), 238–240.
  6. Tyszka, A., Steinhaus’ problem on partition of a triangle, Forum Geom., 7(2007), 181–185.