absolute geometry

English dictionary entry

Meanings

noun

The single (up to logical equivalence) geometry whose axiomatic system is equivalent to that of Euclidean geometry without the parallel postulate or any alternative.
Any geometry whose axiomatic system extends that of absolute geometry (in the singular sense) and neither assumes nor contradicts the parallel postulate.

absolute geometry absolute geometries

From 1832; introduced by Hungarian mathematician János Bolyai (1802—1860).

Euclidean geometry without the parallel postulate

parallel postulate triangle postulate

Japanese: 絶対幾何学 Polish: geometria absolutna Russian: абсолю́тная геоме́трия

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