On Klein's So-called Non-Euclidean geometry

Norbert A'Campo; Athanase Papadopoulos

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arXiv · 1406.7309

On Klein's So-called Non-Euclidean geometry

Norbert A'Campo·Athanase Papadopoulos

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Abstract

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.

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Norbert A'Campo, Athanase Papadopoulos. 2014-06-27. On Klein's So-called Non-Euclidean geometry. https://arxiv.org/abs/1406.7309

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