Isogonal conjugation in isosceles tetrahedron
Saro Harutyunyan
TL;DR
This paper explores the properties of isogonal conjugation in isosceles tetrahedra, revealing geometric structures and invariance properties related to conjugate points and the circumsphere.
Contribution
It introduces new geometric insights into isogonal conjugation in isosceles tetrahedra, including the discovery of hyperbolic paraboloids and invariance of the circumsphere.
Findings
Identification of three hyperbolic paraboloids formed by conjugate points
Proof that the circumsphere remains invariant under isogonal conjugation
Symmetry properties of conjugate points in the tetrahedron
Abstract
In this article we investigate the properties of isogonal conjugation in isosceles tetrahedron. Particularly we reveal three hyperbolic paraboloids each of which is formed by pairs of isogonal conjugate points symmetric in the respective bimedian, as well as we prove that the circumsphere of an isosceles tetrahedron is invariant under isogonal conjugation in that tetrahedron.
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Taxonomy
TopicsMathematics and Applications · Analytic and geometric function theory · Geometric and Algebraic Topology