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A sphere has positive Gaussian curvature everywhere, in 3D. You don't need to view it from 4D to discover this, you can draw a triangle on the surface and note
by SAI_Peregrinus 7y ago
A sphere has positive Gaussian curvature everywhere, in 3D. You don't need to view it from 4D to discover this, you can draw a triangle on the surface and note that the interior angles add up to >180 degrees. You can't project it into 2D space and keep the curvature, which is why all maps have distortion.