Some Properties of the Exeter Transformation

Peter Csiba and László Németh
Additional contact information
Peter Csiba: Department of Mathematics, J. Selye University, 945 01 Komárno, Slovakia
László Németh: Institute of Mathematics, University of Sopron, 9400 Sopron, Hungary

Mathematics, 2021, vol. 9, issue 7, 1-13

Abstract: The Exeter point of a given triangle A B C is the center of perspective of the tangential triangle and the circummedial triangle of the given triangle. The process of the Exeter point from the centroid serves as a base for defining the Exeter transformation with respect to the triangle A B C , which maps all points of the plane. We show that a point, its image, the symmedian, and three exsymmedian points of the triangle are on the same conic. The Exeter transformation of a general line is a fourth-order curve passing through the exsymmedian points. We show that each image point can be the Exeter transformation of four different points. We aim to determine the invariant lines and points and some other properties of the transformation.

Keywords: Exeter transformation; Exeter point; barycentric coordinates (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/9/7/721/pdf (application/pdf)
https://www.mdpi.com/2227-7390/9/7/721/ (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:9:y:2021:i:7:p:721-:d:524743

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 ().