On Some Properties of the First Brocard Triangle in the Isotropic Plane

Autor:	Vladimir Volenec, Zdenka Kolar-Begović, Ružica Kolar-Šuper
Jazyk:	angličtina
Rok vydání:	2022
Předmět:	isotropic plane first Brocard triangle Brocard circle parallelogy Mathematics QA1-939
Zdroj:	Mathematics, Vol 10, Iss 9, p 1381 (2022)
Druh dokumentu:	article
ISSN:	2227-7390
DOI:	10.3390/math10091381
Popis:	In this paper we introduce the first Brocard triangle of an allowable triangle in the isotropic plane and derive the coordinates of its vertices in the case of a standard triangle. We prove that the first Brocard triangle is homologous to the given triangle and that these two triangles are parallelogic. We consider the relationships between the first Brocard triangle and the Steiner axis, the Steiner point, and the Kiepert parabola of the triangle. We also investigate some other interesting properties of this triangle and consider relationships between the Euclidean and the isotropic case.
Databáze:	Directory of Open Access Journals
Externí odkaz:	https://doaj.org/article/8ca8790e93ff4a24a9c1463b9b2b3c7c Zobrazit plný text záznamu View record in DOAJ Plný text ve formátu PDF Plný text ve formátu HTML
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