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Hilbert plane

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In geometry, a Hilbert plane is a model satisfying certain axioms for plane geometry studied by David Hilbert.

Definition

A Hilbert plane consists of a set of point with certain subsets called lines, and certain relations called betweenness for points on a line, congruence for line segments, and congruence for angles. The have to satisfy some (but not all) of Hilbert's axioms.

References

  • Robin Hartshorne, Geometry: Euclid and Beyond, New York: Springer-Verlag, 2000; corrected 4th printing, 2005. ISBN 0-387-98650-2
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