The alpha-version of the Stewart’s theorem

Demonstratio mathematica

article

Özcan Gelişgen¹  Rüstem Kaya¹ 

[1] Department of Mathematics and Computer Sciences, Faculty of Science and Arts, University of Eskisehir Osmangazi

关键词: alpha distance;    alpha plane geometry;    Stewart’s theorem;    median property;   

DOI  :  10.1515/dema-2013-0481

学科分类：外科医学

来源: De Gruyter

【 摘 要 】

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|}+(secα-tanα) min{|x1-x2|,|y1-y2|}$$d_\alpha (P_1 ,P_2 ) = \max \{ \left| {x_1 - x_2 } \right|,\left| {y_1 - y_2 } \right|\} + (\sec \alpha - \tan \alpha )\;\min \{ \left| {x_1 - x_2 } \right|,\left| {y_1 - y_2 } \right|\} $$ where P 1 = ( x 1 , y 1 ) and P 2 = ( x 2 , y 2 ) are two points in analytical plane, and α ∈ [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 a α -analog of formulae for the medians which is the application of Stewart’s theorem.

【 授权许可】

CC BY