The normal line at a point P of a surface σ is the straight

| August 30, 2017

Question
1. The normal line at a point P of a surface σ is the straight line passing through
P parallel to the normal N of σ at P. Prove that:
(i) If the normal lines are all parallel, then σ is an open subset of a plane.
(ii) If all the normal lines pass through some fixed point, then σ is an open subset
of a sphere.

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