Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

The Structure of n Harmonic Points and Generalizations of Desargues’ Theorems

Version 1 : Received: 19 March 2021 / Approved: 22 March 2021 / Online: 22 March 2021 (13:22:18 CET)

A peer-reviewed article of this Preprint also exists.

Thaqi, X.; Aljimi, E. The Structure of n Harmonic Points and Generalization of Desargues’ Theorems. Mathematics 2021, 9, 1018. Thaqi, X.; Aljimi, E. The Structure of n Harmonic Points and Generalization of Desargues’ Theorems. Mathematics 2021, 9, 1018.

Journal reference: Mathematics 2021, 9, 1018
DOI: 10.3390/math9091018

Abstract

In this paper, we consider the relation of more than four harmonic points in a line. For this purpose, starting from the dependence of the harmonic points, Desargues’ theorems, and perspectivity, we note that it is necessary to conduct a generalization of the Desargues’ theorems for projective complete n-points, which are used to implement the definition of the generalization of harmonic points. We present new findings regarding the uniquely determined and constructed sets of H-points and their structure. The well-known fourth harmonic points represent the special case (n=4) of the sets of H-points of rank 2, which is indicated by P42.

Keywords

Projective transformations; Perspectivity; Harmonic points; Generalized Desargues theorems; Harmonic points; Set of H-points rank k

Subject

MATHEMATICS & COMPUTER SCIENCE, Algebra & Number Theory

Comments (0)

We encourage comments and feedback from a broad range of readers. See criteria for comments and our diversity statement.

Leave a public comment
Send a private comment to the author(s)
Views 0
Downloads 0
Comments 0
Metrics 0


×
Alerts
Notify me about updates to this article or when a peer-reviewed version is published.
We use cookies on our website to ensure you get the best experience.
Read more about our cookies here.