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Euclidean geometry is based on flat surfaces and includes the Parallel Postulate, which states that through a point not on a line, exactly one parallel line can be drawn. In contrast, spherical geometry operates on a curved surface where the concept of parallel lines does not exist; any two great circles (the equivalent of straight lines on a sphere) will intersect. In spherical geometry, triangles have angles that sum to more than 180 degrees, unlike in Euclidean geometry, where the angles of a triangle always sum to exactly 180 degrees. Thus, the fundamental properties and the behavior of lines and angles differ significantly between the two geometries.

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1w ago

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