Euclidean geometry follows Euclid's postulates, including the parallel postulate, while non-Euclidean geometry alters this postulate, resulting in curved spaces like in spherical geometry.
Euclidean geometry is the traditional geometry system based on Euclid's postulates, including the parallel postulate, while non-Euclidean geometry is a different geometric system that rejects or alters this parallel postulate, leading to curved spaces and diverse mathematical outcomes. An example of non-Euclidean geometry is spherical geometry, which takes place on the surface of a sphere, where the sum of the interior angles of a triangle can exceed 180 degrees, contrary to Euclidean geometry.
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