Revista de la
Unión Matemática Argentina
An application of Pappus' Involution Theorem to Cayley–Klein projective models
Rubén Vigara
Volume 59, no. 1 (2018), pp. 143–156

DOI: https://doi.org/10.33044/revuma.v59n1a07

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Abstract

Pappus' Involution Theorem is useful for proving incidence relations in the hyperbolic and elliptic planes. This fact is exemplified with the proof of a theorem about a family of $4$-gons in the hyperbolic and elliptic planes. This non-Euclidean theorem is also re-interpreted in multiple ways, providing some other theorems for different figures in the hyperbolic plane.