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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.
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