> And the Pythagorean theorem is a universal truth that holds everywhere. Or at least in every world where there exist straight lines, yes? For instance: > Th

> And the Pythagorean theorem is a universal truth that holds everywhere. Or at least in every world where there exist straight lines, yes? For instance: > The Pythagorean theorem is derived from the axioms of Euclidean geometry, and in fact, were the Pythagorean theorem to fail for some right triangle, then the plane in which this triangle is contained cannot be Euclidean. More precisely, the Pythagorean theorem implies, and is implied by, Euclid's Parallel (Fifth) Postulate.[59][60] Thus, right triangles in a non-Euclidean geometry[61] do not satisfy the Pythagorean theorem. For example, in spherical geometry, all three sides of the right triangle (say a, b, and c) bounding an octant of the unit sphere have length equal to π/2, and all its angles are right angles, which violates the Pythagorean theorem because {\displaystyle a^{2}+b^{2}=2c^{2}>c^{2}}. https://en.wikipedia.org/wiki/Pythagorean_theorem#Non-Euclidean_geometry https://en.wikipedia.org/wiki/Pythagorean_theorem#Non-Euclid...