The definition of spherical geometry is that there are no parallel lines (as far as I know). But isn't that definiton violated with lines such as lines of lattitude? Or are lines of lattitude in fact not straight?
2026-03-26 03:11:42.1774494702
Are Lines of Lattitude Exceptions to Parallel Postulate on Spheres?
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"Lines" in spherical geometry are great circles, i.e. circles formed by intersecting the sphere with a plane which passes through the center of the sphere. Lines of lattitude (except for the equator) are not great circles, so they are not considered lines in spherical geometry.
Separately, it is horribly incorrect to say "The definition of spherical geometry is that there are no parallel lines". It is true that in spherical geometry there are no parallel lines, but this certainly isn't the definition of spherical geometry.