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searching for parallel postulate 6 found (108 total)

alternate case: Parallel postulate

Dehn plane (641 words) [view diff] exact match in snippet view article find links to article

which takes values in Ω(t), gives a model of Euclidean geometry. The parallel postulate is true in this model, but if the deviation from the perpendicular
Jeremiah J. Callahan (1,424 words) [view diff] no match in snippet view article find links to article
Critique of Metageometry claimed to have proved Euclid's fifth "parallel" postulate, by re-ordering the logical structure of Euclid's Elements. Callahan
Nonstandard analysis (3,978 words) [view diff] exact match in snippet view article find links to article
(analogous to the Dehn plane) is external, and in this limited plane the parallel postulate is violated. For example, any line passing through the point (0, 1)
How Not to Be Wrong (2,058 words) [view diff] exact match in snippet view article find links to article
Universe": This chapter talks about János Bolyais, and his work on the parallel postulate. Others mentioned in this chapter include David Hilbert, and Gottlob
Joseph Delboeuf (2,300 words) [view diff] case mismatch in snippet view article find links to article
ISBN 9789027718372 BEESON, MICHAEL (2016). "Constructive Geometry and the Parallel Postulate". The Bulletin of Symbolic Logic. 22 (1): 1–104. arXiv:1407.4398.
Glossary of classical algebraic geometry (11,193 words) [view diff] exact match in snippet view article find links to article
2.  Absolute geometry is roughly Euclidean geometry without the parallel postulate. accidental An accidental (or improper) double point of a surface