English Dictionary

absolute geometry

noun

(geometry) The single (up to logical equivalence) geometry whose axiomatic system is equivalent to that of Euclidean geometry without the parallel postulate or any alternative.

Absolute geometry is a branch of mathematics that deals with the properties and relationships of geometric figures in a space that is not influenced by any specific coordinate system.

意味（1）

(geometry) The single (up to logical equivalence) geometry whose axiomatic system is equivalent to that of Euclidean geometry without the parallel postulate or any alternative.

Recall that absolute geometry is the set of statements that can be deduced from Euclid's first four postulates. Then existence of parallel lines is certainly a theorem of absolute geometry, while the question being addressed by most of the mathematicians discussed in this section is whether uniqueness of parallels is also a theorem of absolute geometry.

意味（2）

(geometry) Any geometry whose axiomatic system extends that of absolute geometry (in the singular sense) and neither assumes nor contradicts the parallel postulate.

A discussion of one-dimensional absolute geometries, with examples, will be given in a separate paper.