Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed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

How to cite: Thaqi, X.; (Alimi), E.A. The Structure of n Harmonic Points and Generalizations of Desargues’ Theorems. Preprints 2021, 2021030537 (doi: 10.20944/preprints202103.0537.v1). Thaqi, X.; (Alimi), E.A. The Structure of n Harmonic Points and Generalizations of Desargues’ Theorems. Preprints 2021, 2021030537 (doi: 10.20944/preprints202103.0537.v1).

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.

Subject Areas

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

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