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