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

Author

Listed:
  • 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)

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 .

Suggested Citation

  • Xhevdet Thaqi & Ekrem Aljimi, 2021. "The Structure of n Harmonic Points and Generalization of Desargues’ Theorems," Mathematics, MDPI, vol. 9(9), pages 1-15, April.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:9:p:1018-:d:547047
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