Geometry which depends only on the first four of Euclid's postulates and not on the parallel postulate. Euclid himself used only the first four postulates for the first 28 propositions of the Elements, but was forced to invoke the parallel postulate on the 29th.
Absolute Geometry
See also
Affine Geometry, Elements, Euclid's Postulates, Geometry, Ordered Geometry, Parallel PostulateExplore with Wolfram|Alpha
References
Hofstadter, D. R. Gödel, Escher, Bach: An Eternal Golden Braid. New York: Vintage Books, pp. 90-91, 1989.Referenced on Wolfram|Alpha
Absolute GeometryCite this as:
Weisstein, Eric W. "Absolute Geometry." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/AbsoluteGeometry.html