Definition:Parallel (Geometry)/Surfaces

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Definition

Let $S_1$ and $S_2$ be surfaces in ordinary space.

Let $S_1$ and $S_2$ have the property that:

for every point $P$ on $S_1$, a normal vector passing through $P$ is also a normal vector to $S_2$

and:

for every point $Q$ on $S_2$, a normal vector passing through $Q$ is also a normal vector to $S_1$.


Then $S_1$ and $S_2$ are parallel.





Also see

  • Results about parallel surfaces can be found here.


Sources