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

Vladimir Volenec, Zdenka Kolar-Begović and Ružica Kolar-Šuper
Additional contact information
Vladimir Volenec: Department of Mathematics, University of Zagreb, Bijenička cesta 30, 10 000 Zagreb, Croatia
Zdenka Kolar-Begović: Department of Mathematics, University of Osijek, Trg Lj. Gaja 6, 31 000 Osijek, Croatia
Ružica Kolar-Šuper: Faculty of Education, University of Osijek, Cara Hadrijana 10, 31 000 Osijek, Croatia

Mathematics, 2022, vol. 10, issue 9, 1-13

Abstract: 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.

Keywords: isotropic plane; first Brocard triangle; Brocard circle; parallelogy (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/9/1381/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/9/1381/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:9:p:1381-:d:797895

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().