English Dictionary

absolute geometry

名詞

(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.

日本語の意味

絶対幾何学―平行公理（または平行に関するいかなる仮定）を除いたユークリッド幾何学と同等の公理系を持つ、論理的に一意な（論理的同値における）幾何学体系。

In his lecture, he emphasized how absolute geometry provides the common foundation for results in both Euclidean and hyperbolic settings.

彼の講義では、ユークリッド幾何学の公理系から平行公理やそれに代わるものを除いたものと論理的に同値である、論理的同値の範囲で唯一の幾何学としての絶対幾何学が、ユークリッド幾何学と双曲幾何学の両方の結果に共通する基盤を提供することが強調された。

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.

absolute geometries （ plural ）