Characterization of an Isosceles Tetrahedron

被引：0

作者：

Katsuura, Hidefumi ^{[1
]}

机构：

[1] San Jose State Univ, Dept Math & Stat, One Washington Sq, San Jose, CA 95192 USA

来源：

JOURNAL FOR GEOMETRY AND GRAPHICS | 2019年 / 23卷 / 01期

关键词：

Isosceles tetrahedron; in-center; ex-center; centroid; circum-center;

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A tetrahedron in which each edge is equal to its opposite is an isosceles tetrahedron. We will use vectors to prove the following statement: A tetrahedron OABC is isosceles if, and only if the centroid of the parallelepiped defined by the three edges OA, OB, and OC is an ex-center of the tetrahedron OABC.

引用

页码：37 / 40

页数：4

共 22 条

[1] Isosceles Tetrahedron and an Equimomental System of a Rigid Body
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VESTNIK ST PETERSBURG UNIVERSITY-MATHEMATICS, 2023, 56 (01) : 119 - 124
[2] Morley’s trisector Theorem for isosceles tetrahedron
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Acta Mathematica Hungarica, 2021, 165 : 308 - 315
[3] Morley's trisector Theorem for isosceles tetrahedron
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[4] In and Ex Spheres of a Tetrahedron
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[5] Rotation of Isosceles Tetrahedron in Central Newtonian Force Field: Staude Cone
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[6] Rotation of Isosceles Tetrahedron in Central Newtonian Force Field: Staude Cone
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[7] On Stationary Motions of an Isosceles Tetrahedron with a Fixed Point in the Central Field of Forces
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[8] On Stationary Motions of an Isosceles Tetrahedron with a Fixed Point in the Central Field of Forces
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MECHANICS OF SOLIDS, 2022, 57 (07) : 1620 - 1632
[9] Stationary Motions of a Close to Regular Isosceles Tetrahedron with a Fixed Point in the Central Newtonian Force Field
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[10] Stationary Motions of a Close to Regular Isosceles Tetrahedron with a Fixed Point in the Central Newtonian Force Field
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Mechanics of Solids, 2022, 57 : 1059 - 1067

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