imaginary geometry

Meanings

1. Absolute geometry, an axiomatised geometry in which the parallel postulate is absent and not replaced by an alternative, and of which Euclidean geometry and some non-Euclidean geometries are subtypes.

Etymology

Calque of Russian мни́мая геометрия (mnímaja geometrija), coined by mathematician Nicolai Lobachevsky, probably influenced by мни́мое чи́сло (mnímoje číslo, “imaginary number”), although his precise reasoning is unknown.