absolute geometry
Word Rarity
Rare
Frequency: 3.79 in modern English
24
Scrabble Score
16
Letters
7
Syllables
12
Unique Chars
Meaning
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.
noun
Any geometry whose axiomatic system extends that of absolute geometry (in the singular sense) and neither assumes nor contradicts the parallel postulate.
Example Sentences
- "1993 [Princeton University Press], Donald M. Davis, The Nature and Power of Mathematics, 2004, Dover, page 85, 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."
- "1970, J. F. Rigby, Axioms for Absolute Geometry, III, Canadian Journal of Mathematics, Vol. XXII, No. 1, Canadian Mathematical Congress, University of Toronto Press, page 185, A discussion of one-dimensional absolute geometries, with examples, will be given in a separate paper."
Etymology
Inflected Forms
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Frequently Paired Words
Synonyms
Euclidean geometry without the parallel postulate