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

Mathematics

Ekrem Aljimi¹  Xhevdet Thaqi¹ 

[1] Faculty of Applied Sciences, Public University “Kadri Zeka”, 60000 Gjilan, Kosovo;

关键词: projective transformations;    perspectivity;    harmonic points;    generalization of Desargues’ theorems;    complete plane n-point;    set of H-points rank k;   

DOI  :  10.3390/math9091018

来源: DOAJ

【 摘 要 】

: 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.

【 授权许可】

Unknown