The median triangle theorem as an entrance to certain issues in higher-dimensional geometry

被引：0
作者：
Hajja M. [1 ]
Krasopoulos P.T. [2 ]
Martini H. [3 ]
机构：
[1] P.O. Box 388 (Al-Husun), Irbid
[2] Department of Informatics, KEAO, Electronic National Social Security Fund, 12 Patision St., Athens
[3] Faculty of Mathematics, Chemnitz University of Technology, Chemnitz
来源：
Mathematische Semesterberichte | 2022年 / 69卷 / 1期
关键词：
Apollonius; theorem; Centroid; Median triangle theorem; Pompeiu’s theorem; Simplex; Tetrahedron;
D O I：
10.1007/s00591-021-00308-5
中图分类号：
学科分类号：
摘要：
The median triangle theorem states that the three medians of a triangle can serve as the sides of another triangle. This theorem together with other related results from plane geometry are presented, and intriguing questions are set about analogues in higher dimensions. Answers to these questions are also presented, and by this way a reader can smoothly enter to certain issues of tetrahedral and then higher-dimensional geometry. © 2021, Springer-Verlag GmbH Deutschland, ein Teil von Springer Nature.
引用
收藏
页码：19 / 40
页数：21
相关论文
共 36 条
[1]  
Abrosimov N.V., Makai E., Mednykh A.D., Nikonorov Y.G., Rote G., The infimum of the volumes of convex polytopes of any given facet areas is 0, Stud. Sci. Math. Hung., 51, pp. 466-519, (2014)
[2]  
Aigner M., Ziegler G.M., Proofs from THE BOOK, (2004)
[3]  
Al-Afifi G., Hajja M., Hamdan A., Another n-dimensional generalization of Pompeiu’s theorem, Am. Math. Mon., 125, pp. 612-622, (2018)
[4]  
Al-Afifi G., Hajja M., Hamdan A., Krasopoulos P.T., Pompeiu-like theorems for the medians of a simplex, Math. Inequal. Appl., 21, pp. 539-552, (2018)
[5]  
Altshiller-Court N., Modern Pure Solid Geometry, (1964)
[6]  
Andreescu T., Korsky S., Pohoata C., Lemmas in Olympiad Geometry, (2016)
[7]  
Balk M.B., Boltyanskij V.G., Geometry of Masses. (Geometriya mass), 61, (1987)
[8]  
Berger M., Geometry I, (1994)
[9]  
Blumenthal L.M., A budget of curiosa metrica, Am. Math. Mon., 66, pp. 453-460, (1959)
[10]  
Carter B., The i-centroid of an n-simplex, Am. Math. Mon., 68, pp. 914-917, (1961)
1234