Is there a form of non-Euclidean geometry in which perpendicular lines never cross, or cross twice or something?
2026-03-25 23:51:00.1774482660
Euclid's Perpendicular Postulate
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Perpendicular lines are by definition those that meet at a right angle. Hence "never cross" is impossible. Non-Euclidean geometries are those that differ in the variation of the parallel postulate; especially, it holds in all of them that two distinct points determine a line so that "cross twice" is also impossible.