absolute geometry
The term "absolute geometry" refers to a foundational area in mathematics that studies properties valid in both Euclidean and non-Euclidean geometries, introduced by János Bolyai in 1832.
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Definition
C2Mathematics
(technical, academic)A branch of geometry based on all of Euclid's axioms except the one about parallel lines.
Example
- Absolute geometry serves as a common foundation for both Euclidean and hyperbolic geometries.
C2Mathematics
(technical, academic)A field of study that explores properties and theorems true in both Euclidean and hyperbolic geometries without assuming the parallel postulate.
Example
- Many of Euclid's propositions are valid within the framework of absolute geometry.
Similar
Terms that have similar or relatively close meanings to "absolute geometry":
absolute formfinite geometrycomplex geometrycontact geometryabsolute weightspherical geometryaffine geometryabsolute stateabsolute constantabsolute reality