Geometric Inversion, Cross Ratio, Projective Geometry and Poincaré Disk Model

Autor:	Salvatore Capozziello, Wladimir-Georges Boskoff
Rok vydání:	2020
Předmět:	symbols.namesake Poincaré disk model Mathematical analysis Euclidean geometry Cross-ratio symbols Projective test Invariant (mathematics) Projective geometry Mathematics
Zdroj:	A Mathematical Journey to Relativity ISBN: 9783030478933
DOI:	10.1007/978-3-030-47894-0_3
Popis:	This chapter is devoted to a first model of Non-Euclidean Geometry. To construct this model, we need to deal with one of the most important transformations of the Euclidean plane, the geometric inversion. We still need some other acquirements, therefore we meet the Projective Geometry. An invariant described by a special projective map of a circle allows us to construct a non-Euclidean distance inside the disk. Elaborating the previous model we highlight the Poincare disk model.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::2cf1891d76b2bc23522eb8eac4d8452b https://doi.org/10.1007/978-3-030-47894-0_3 Zobrazit plný text záznamu