2014/06/27 by Norbert A’Campo, Athanase Papadopoulos, A'Campo, Norbert +1
Mathematics · Physics and Astronomy · #FOS: Mathematics #Geometric Topology (math.GT) #History and Theory of Mathematics #Mathematics and Applications #Metric Geometry (math.MG) #Relativity and Gravitational Theory
paper · doi:10.48550/arxiv.1406.7309
openalex publication_date 2014/06/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In two papers titled "On the so-called non-Euclidean geometry", I and II, Felix Klein proposed a construction of the spaces of constant curvature -1, 0 and and 1 (that is, hyperbolic, Euclidean and spherical geometry) within the realm of projective geometry. Klein's work was inspired by ideas of Cayley who derived the distance between two points and the angle between two planes in terms of an arbitrary fixed conic in projective space. We comment on these two papers of Klein and we make relations with other works.