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Preserved in Portico This version is not peer-reviewed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.
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
Computer Science and Mathematics, Algebra and Number Theory
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Comments (0)
We encourage comments and feedback from a broad range of readers. See criteria for comments and our Diversity statement.
Leave a public commentSend a private comment to the author(s)
* All users must log in before leaving a comment
