关于欧氏平面ℝ²中三角形的John定理
The John Theorem for Triangles in 2-Dimension Euclidean Space ℝ²
DOI: 10.12677/AAM.2019.85109, PDF,    国家自然科学基金支持
作者: 马统一：河西学院数学与统计学院，甘肃 张掖；肖 添：海南大学数学系信息与计算科学2016级1班，海南 海口
关键词: 三角形；Hohn椭圆；John定理；重心坐标；Triangle； John Theorem； John Ellipse； Barycentric Coordinates
摘要: 本文利用著名的John定理研究三角形的极值性质，刻画了正三角形的John接触点的特征，证明了任意一个三角形的John椭圆是圆当且仅当该三角形是正三角形。
Abstract: In this paper, a description of the John contact points of a regular triangle was given. It was proved that the John ellipse of any triangle is circle if and only if this triangle is regular and that the John ellipse of a regular triangle is its inscribed circle.
文章引用：马统一, 肖添. 关于欧氏平面ℝ²中三角形的John定理[J]. 应用数学进展, 2019, 8(5): 958-964. https://doi.org/10.12677/AAM.2019.85109

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