A Characteristic of Similarities by Use of Steinhaus’ Problem on Partition of Triangles

Year 2020, Volume: 8 Issue: 1, 117 - 122, 20.03.2020

Oğuzhan Demirel Leyla Aslan Damla Topal

https://doi.org/10.36753/mathenot.615168

Abstract

H. Steinhaus [1] 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 new characteristic of similarities by use of
the Steinhaus’ Problem on partition of a triangle. 

Keywords

Möbius transformation, Similarity, Steinhaus’ problem

References

• [1] Steinhaus, H., Problem No. 779 (in Polish), Matematyka, 19 (1966) 92.
• [2] Haruki, H., Rassias, T.M., A new characteristic of Möbius transformations by use of Apollonius points of triangles. J. Math. Anal. Appl.197 (1996), no. 1, 14--22.
• [3] Haruki, H., Rassias, T.M., A new characteristic of Möbius transformations by use of Apollonius quadrilaterals. Proc. Amer. Math. Soc. 126 (1998), no. 10, 2857--2861.
• [4] Bulut, S., Özgür, N.Y., A new characteristic of Möbius transformations by use of Apollonius points of pentagons. Turkish J. Math. 28 (2004), no. 3, 299--305.
• [5] Haruki, H., Rassias, T.M., A new characterization of Möbius transformations by use of Apollonius hexagons. Proc. Amer. Math. Soc. 128 (2000), no. 7, 2105--2109.
• [6] Tyszka, A. Steinhaus' problem on partition of a triangle. Forum Geom.7 (2007), 181-185.
• [7] Pennisi, L.L., Gordon, L.I., Lasher, S., Elements of Complex Variables, Holt, Rinehart&Winston, New York, 1963.
• [8] Nevanlinna, R., Paatero, V., Introduction to Complex Analysis, Addison-Wesley, New York, 1964.