Classificação das geometrias: um diálogo entre os textos de Arthur Cayley e de Felix Klein

Leandro Silva Dias; Gérard Emile Grimberg

doi:10.53727/rbhc.v12i2.59

Authors

Leandro Silva Dias Universidade Federal do Rio de Janeiro (UFRJ)
Gérard Emile Grimberg Universidade Federal do Rio de Janeiro (UFRJ)

DOI:

https://doi.org/10.53727/rbhc.v12i2.59

Keywords:

History of non-Euclidean geometry, Arthur Cayley, Felix Klein, metric, models

Abstract

Traditionally, when it comes to non-Euclidean geometries, most historians report that Felix Klein was inspired by reading Arthur Cayley’s A Sixth Memoir upon Quantics (1859). However, they do not fully present Cayley’s contributions, only saying that Klein applied Cayley’s work to the case of non-Euclidean geometries. However, there are some problems in this narrative, the biggest of which is that Cayley has his own approach that is slightly different from that presented by Klein. Our article proposes to analyze these differences, clarifying the relation between the works of these mathematicians and the genesis of non – Euclidean metrics.