Original scientific paper

https://doi.org/10.31896/k.28.1

On Permutations of Desarguesian Sextuples

Kostantinos Myrianthis ; 58, Zan Moreas street, 15231 Athens, Greece *
Hellmuth Stachel ; Vienna University of Technology, Vienna, Austria

* Corresponding author.

Abstract

Desargues's theorem plays an essential role at the axiomatic foundations of Projective Geometry. The configuration behind this theorem contains ten lines, the sides of two triangles, three lines through the center and the axis. We focus on the ordered sextuple of intersection points with the axis and call it Desarguesian. A permutation of this sextuple is called admissible if it preserves the property of being Desarguesian. Some permutations are admissible only if Pappus's theorem holds in the plane. Under this assumption we can prove that for each permutation there exist particular Desarguesian sextuples which remain Desarguesian under the permutation.

Keywords

Desargues's theorem; Pappus's theorem; Desarguesian sextuple; involution

Hrčak ID:

323749

URI

https://hrcak.srce.hr/323749

Publication date:

20.12.2024.

Article data in other languages: croatian

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