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## Demonstratio Mathematica

Tytuł artykułu

### The alpha-version of the Stewart's theorem

Autorzy Gelişgen, Ö.  Kaya, R.
Treść / Zawartość https://www.degruyter.com/view/j/dema
Warianty tytułu
Języki publikacji EN
Abstrakty
 EN G. Chen [1] developed Chinese checker metric for the plane on the question “how to develop a metric which would be similar to the movement made by playing Chinese checker” by E. F. Krause [13]. Tian [17] developed α-metric which is defined by dα(P1,P2)=max {|x1 - x2|, |y1 - y2|} + (sec α - tanα) min {|x1 - x2|, |y1 - y2|} where P1= (x1, y1) and P2= (x2, y2) are two points in analytical plane, and α ϵ [0, π/4]. Stewart’s theorem yields a relation between lengths of the sides of a triangle and the length of a cevian of the triangle. A taxicab and Chinese checkers analogues of Stewart’s theorem are given in [12] and [9], respectively. In this work, we give an α-analog of the theorem of Stewart by using the base line concept and we give α-analog of formulae for the medians which is the application of Stewart’s theorem.
Słowa kluczowe
 PL odległość alfa   geometria płaszczyzny alfa   twierdzenie Stewarta   właściwości mediany EN alpha distance   alpha plane geometry   Stewart's theorem   median property
Wydawca De Gruyter
Czasopismo Demonstratio Mathematica
Rocznik 2013
Tom Vol. 46, nr 4
Strony 795--808
Opis fizyczny Bibliogr. 17 poz., rys., tab., wykr.
Twórcy
 autor Gelişgen, Ö. Department of Mathematics and Computer Sciences, Faculty of Science and Arts, University of Eskisehir Osmangazi, Eskisehir, Turkey, gelisgen@ogu.edu.tr autor Kaya, R. Department of Mathematics and Computer Sciences, Faculty of Science and Arts, University of Eskisehir Osmangazi, Eskisehir, Turkey, rkaya@ogu.edu.tr
Bibliografia
[1] G. Chen, Lines and Circles in Taxicab Geometry, Master Thesis, Department of Mathematics and Computer Science, Central Missouri State Univ., 1992.
[2] H. S. M. Coxeter, S. L. Greitzer, Geometry Revisited, The Mathematical Association of America, 1967.
[3] H. B. Çolakoğlu, Ö. Gelişgen, R. Kaya, Pythagorean theorems in the alpha plane, Math. Commun. 14(2) (2009), 211–221.
[4] B. Divjak, Notes on taxicab geometry, Scientific and Professional Information Journal of Croatian Society for Constructive Geometry and Computer Graphics (KoG) 5 (2000), 5–9.
[5] Ö. Gelisgen, Minkowski Geometrileri Üzerine: Taksi, Çin Dama ve-Geometrileri Hakkında Genel Bir Analiz, Phd Thesis, Eskişehir Osmangazi University, 2007.
[6] Ö. Gelişgen, R. Kaya, CC-analog of the theorem of Pythagoras, Algebras Groups Geom. 23(2) (2006), 179–188.
[7] Ö. Gelişgen, R. Kaya, On distance in three dimensional space, Appl. Sci. 8 (2006), 65–69.
[8] Ö. Gelişgen, R. Kaya, Generalization of distance to n-dimensional space, Scientific and Professional Journal of the Croatian Society for Geometry and Graphics (KoG) 10 (2006), 33–37.
[9] Ö. Gelişgen, R. Kaya, The CC-version of the Stewart’s theorem, Appl. Sci. 11 (2009), 68–77.
[10] R. Kaya, Ö. Gelişgen, S. Ekmekçi, A. Bayar, Group of isometries of CC-plane, Missouri J. Math. Sci. 18(3) (2006), 221–233.
[11] R. Kaya, Ö. Gelişgen, S. Ekmekçi, A. Bayar, On the group of isometries of the plane with generalized absolute value metric, Rocky Mountain J. Math. 39(2) (2009), 591–604.
[12] R. Kaya, H. B. Colakoglu, Taxicab versions of some Euclidean theorems, Int. J. Pure Appl. Math. 26(1) (2006), 69–81.
[13] E. F. Krause, Taxicab Geometry, Addision-Wesley, Menlo Park, California, 1975.
[14] M. Özcan, R. Kaya, Area of a triangle in terms of the taxicab distance, Missouri J. Math. Sci. 15(3) (2003), 178–185.
[15] R. S. Milmann, G. D. Parker, Geometry; A Metric Approach with Models, Springer, 1991.
[16] A. C. Thompson, Minkowski Geometry, Cambridge University Press, 1996.
[17] S. Tian, Alpha distance – a generalization of Chinese checker distance and taxicab distance, Missouri J. Math. Sci. 17(1) (2005), 35–40.
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