Research Article

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

Volume: 8 Number: 1 March 20, 2020
Oğuzhan Demirel *, Leyla Aslan , Damla Topal
EN

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

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. [1] Steinhaus, H., Problem No. 779 (in Polish), Matematyka, 19 (1966) 92.
  2. [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. [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. [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. [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. [6] Tyszka, A. Steinhaus' problem on partition of a triangle. Forum Geom.7 (2007), 181-185.
  7. [7] Pennisi, L.L., Gordon, L.I., Lasher, S., Elements of Complex Variables, Holt, Rinehart&Winston, New York, 1963.
  8. [8] Nevanlinna, R., Paatero, V., Introduction to Complex Analysis, Addison-Wesley, New York, 1964.
APA
Demirel, O., Aslan, L., & Topal, D. (2020). A Characteristic of Similarities by Use of Steinhaus’ Problem on Partition of Triangles. Mathematical Sciences and Applications E-Notes, 8(1), 117-122. https://doi.org/10.36753/mathenot.615168
AMA
1.Demirel O, Aslan L, Topal D. A Characteristic of Similarities by Use of Steinhaus’ Problem on Partition of Triangles. Math. Sci. Appl. E-Notes. 2020;8(1):117-122. doi:10.36753/mathenot.615168
Chicago
Demirel, Oğuzhan, Leyla Aslan, and Damla Topal. 2020. “A Characteristic of Similarities by Use of Steinhaus’ Problem on Partition of Triangles”. Mathematical Sciences and Applications E-Notes 8 (1): 117-22. https://doi.org/10.36753/mathenot.615168.
EndNote
Demirel O, Aslan L, Topal D (March 1, 2020) A Characteristic of Similarities by Use of Steinhaus’ Problem on Partition of Triangles. Mathematical Sciences and Applications E-Notes 8 1 117–122.
IEEE
[1]O. Demirel, L. Aslan, and D. Topal, “A Characteristic of Similarities by Use of Steinhaus’ Problem on Partition of Triangles”, Math. Sci. Appl. E-Notes, vol. 8, no. 1, pp. 117–122, Mar. 2020, doi: 10.36753/mathenot.615168.
ISNAD
Demirel, Oğuzhan - Aslan, Leyla - Topal, Damla. “A Characteristic of Similarities by Use of Steinhaus’ Problem on Partition of Triangles”. Mathematical Sciences and Applications E-Notes 8/1 (March 1, 2020): 117-122. https://doi.org/10.36753/mathenot.615168.
JAMA
1.Demirel O, Aslan L, Topal D. A Characteristic of Similarities by Use of Steinhaus’ Problem on Partition of Triangles. Math. Sci. Appl. E-Notes. 2020;8:117–122.
MLA
Demirel, Oğuzhan, et al. “A Characteristic of Similarities by Use of Steinhaus’ Problem on Partition of Triangles”. Mathematical Sciences and Applications E-Notes, vol. 8, no. 1, Mar. 2020, pp. 117-22, doi:10.36753/mathenot.615168.
Vancouver
1.Oğuzhan Demirel, Leyla Aslan, Damla Topal. A Characteristic of Similarities by Use of Steinhaus’ Problem on Partition of Triangles. Math. Sci. Appl. E-Notes. 2020 Mar. 1;8(1):117-22. doi:10.36753/mathenot.615168