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

Xhevdet Thaqi and Ekrem Aljimi
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Xhevdet Thaqi: Faculty of Applied Sciences, Public University “Kadri Zeka”, 60000 Gjilan, Kosovo
Ekrem Aljimi: Faculty of Applied Sciences, Public University “Kadri Zeka”, 60000 Gjilan, Kosovo

Mathematics, 2021, vol. 9, issue 9, 1-15

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 P 4 2 .

Keywords: projective transformations; perspectivity; harmonic points; generalization of Desargues’ theorems; complete plane n-point; set of H-points rank k (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2021
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