Glasnik Matematicki, Vol. 40, No.2 (2005), 313-315.
THREE-DIMENSIONAL HYPERBOLIC GEOMETRY WITH PLANES AND
PLANE PARALLELISM AS ONLY PRIMITIVE NOTIONS
Victor Pambuccian
Department of Integrative Studies, Arizona State University - West campus,
P. O. Box 37100, Phoenix AZ 85069-7100, USA
e-mail: pamb@math.west.asu.edu
Abstract. We show that Euclidean Möbius planes can be axiomatized
in terms of circles and circle-tangency, and that 3-dimensional hyperbolic
geometry can be axiomatized in terms of planes and plane-parallelism.
2000 Mathematics Subject Classification.
51M10, 51B10, 03B30.
Key words and phrases. Hyperbolic space, Euclidean Möbius plane, axiom system.
Full text (PDF) (free access)
DOI: 10.3336/gm.40.2.10
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CrossRef
- V. Pambuccian,
Sphere tangency as single primitive notion for
hyperbolic and Euclidean geometry,
Forum Math. 15 (2003), 943-947.
CrossRef
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