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Thin Right Triangle Convexity

Author

Listed:
  • Xiangxiang Nie

    (School of Mathematical Sciences, Hebei Normal University, Shijiazhuang 050024, China
    Hebei Key Laboratory of Computational Mathematics and Applications, Shijiazhuang 050024, China
    Hebei International Joint Research Center for Mathematics and Interdisciplinary Science, Shijiazhuang 050024, China)

  • Liping Yuan

    (School of Mathematical Sciences, Hebei Normal University, Shijiazhuang 050024, China
    Hebei Key Laboratory of Computational Mathematics and Applications, Shijiazhuang 050024, China
    Hebei International Joint Research Center for Mathematics and Interdisciplinary Science, Shijiazhuang 050024, China)

  • Tudor Zamfirescu

    (School of Mathematical Sciences, Hebei Normal University, Shijiazhuang 050024, China
    Hebei International Joint Research Center for Mathematics and Interdisciplinary Science, Shijiazhuang 050024, China
    Fachbereich Mathematik, Technische Universität Dortmund, 44221 Dortmund, Germany
    Roumanian Academy, 014700 Bucharest, Romania)

Abstract

Let F be a family of sets in R d (always d ≥ 2 ). A set M ⊂ R d is called F -convex , if for any pair of distinct points x , y ∈ M , there is a set F ∈ F , such that x , y ∈ F and F ⊂ M . A thin right triangle is the boundary of a non-degenerate right triangle in R 2 . The aim of this paper is to introduce and begin investigating the thin right triangle convexity for short trt -convexity, which is obtained when F is the family of all thin right triangles. We investigate the t r t -convexity of unbounded sets, convex surfaces and planar geometric graphs.

Suggested Citation

  • Xiangxiang Nie & Liping Yuan & Tudor Zamfirescu, 2022. "Thin Right Triangle Convexity," Mathematics, MDPI, vol. 10(22), pages 1-8, November.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:22:p:4170-:d:966161
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