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

Steinhaus' Problem on Partition of a Hyperbolic Triangle

Oğuzhan DEMİREL
Sayfa
98–102
Yayın Tarihi
2018-12-28
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

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

📌 3 Maddede Bu Makale

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Amaç & Hipotez: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.
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Temel Bulgular & Veri: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.
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Sonuç & Katkı:In this paper, we present a solution of this problem in the Poincaré disc model of hyperbolic geometry.
🔬Tür:Modelleme & Sayısal Simülasyon
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler: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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Bu Makaleye Atıf Yap

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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Kaynakça (6)

  1. Ahlfors, L., Complex analysis: An introduction to the theory of analytic functions of one complex variable, Third edition. International Series in Pure and Applied Mathematics. McGraw-Hill Book Co., New York, 1978.
  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.