Abstract
Euclid’s axiom, as formulatedby Hilbert (see Section 1.1), states that given a point A not lying on a line a, there is at most one line passing through A that does not intersect a. Hyperbolic geometry replaced that axiom with the assumption that more than one line through A does not intersect a. These are the only two possibilities consistent with the remaining axioms. From Hilbert’s axioms we can always construct one line through A not meeting a.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1998 Springer Science+Business Media New York
About this chapter
Cite this chapter
Singer, D.A. (1998). Geometry of the Sphere. In: Geometry: Plane and Fancy. Undergraduate Texts in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0607-1_4
Download citation
DOI: https://doi.org/10.1007/978-1-4612-0607-1_4
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6837-6
Online ISBN: 978-1-4612-0607-1
eBook Packages: Springer Book Archive