Abstract
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 Poincaré disk model.
Virtus unita fortior agit.
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Boskoff, WG., Capozziello, S. (2020). Geometric Inversion, Cross Ratio, Projective Geometry and Poincaré Disk Model. In: A Mathematical Journey to Relativity. UNITEXT for Physics. Springer, Cham. https://doi.org/10.1007/978-3-030-47894-0_3
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DOI: https://doi.org/10.1007/978-3-030-47894-0_3
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Publisher Name: Springer, Cham
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Online ISBN: 978-3-030-47894-0
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