Absolute geometry is a geometry based on an axiom system for Euclidean geometry without the parallel postulate or any of its alternatives. Traditionally...

non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean geometry lies at the...

theorems of absolute geometry hold in hyperbolic geometry as well as in Euclidean geometry. Absolute geometry is inconsistent with elliptic geometry: in elliptic...

Victor; Schacht, Celia (2018), "Euler's inequality in absolute geometry", Journal of Geometry, 109 (Art. 8): 1–11, doi:10.1007/s00022-018-0414-6, S2CID 125459983...

resulting geometry is absolute geometry. There are two kinds of absolute geometry, Euclidean and hyperbolic. All theorems of absolute geometry, including...

developed absolute geometry—a geometry that includes both Euclidean geometry and hyperbolic geometry. The discovery of a consistent alternative geometry that...

biotechnology company Absolute (geometry), the quadric at nothing Absolute (perfumery), a fragrance substance produced by solvent extraction Absolute infinite or...

27 of Euclid's Elements, a theorem of absolute geometry (hence valid in both hyperbolic and Euclidean Geometry), proves that if the angles of a pair of...

Elliptic geometry is an example of a geometry in which Euclid's parallel postulate does not hold. Instead, as in spherical geometry, there are no parallel...

in hyperbolic geometry. Similarly, the real line is the absolute of the Poincaré half-plane model. The extent of Cayley–Klein geometry was summarized...