Angle Bisectors of a Triangle in Lorentzian Plane
Joseph Cho
TL;DR
This paper redefines angle bisectors in Lorentzian geometry to enable the study of triangle centers, investigating the existence of the incenter and isogonal conjugates within this non-Euclidean context.
Contribution
It introduces a new definition of angle bisectors in Lorentzian geometry, facilitating the analysis of triangle centers like the incenter and isogonal conjugates.
Findings
Redefinition allows for the study of triangle centers in Lorentzian plane.
Existence conditions for the incenter are established.
Conditions for the isogonal conjugate are analyzed.
Abstract
In Lorentzian geometry, limited definition of angles restricts the use of angle bisectors in study of triangles. This paper redefines angle bisectors so that they can be used to study attributes of triangles. Using the new definition, this paper investigates the existence of the incenter and the isogonal conjugate of a triangle in Lorentzian plane.
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Taxonomy
TopicsMathematics and Applications · Algebraic and Geometric Analysis · History and Theory of Mathematics