Euclidean postulates do not hold true for:
Irregular curved surfaces
Euclid's postulates, such as the existence of a unique straight line between two points and the parallel postulate, were formulated for geometry drawn on a flat plane.
Plane surfaces, coordinate geometry (which is built on the flat Cartesian plane), and triangles (a figure of plane geometry) are all situations where Euclidean postulates apply and hold true.
On irregular curved surfaces, however, the shortest path between two points is no longer a straight line but a curve, and properties such as the angle sum of a triangle being 180 degrees or parallel lines never meeting no longer hold — this is the domain of non-Euclidean geometry.
Hence, Euclidean postulates do not hold true for irregular curved surfaces.
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