Discussion
Which shape cannot be flattened without stretching?
Answer: C
Correct answer: A sphere
A cone and a cylinder are developable surfaces: each can be cut and unrolled flat without stretching or tearing, which is why they serve as intermediate surfaces in projection. A sphere is not, because it has intrinsic curvature that no bending can remove. That single geometric fact - Gauss’s theorema egregium - is why all map distortion exists.
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