Definition:Parallel (Geometry)/Surfaces

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.

This page needs proofreading. In particular: Intuitive, based on the fact that it seems obvious. Consistent with definition for parallel planes. Someone please look it over and see if it makes sense. If you believe all issues are dealt with, please remove {{Proofread}} from the code. To discuss this page in more detail, feel free to use the talk page. When this work has been completed, you may remove this instance of {{Proofread}} from the code.

Also see

• Results about parallel surfaces can be found here.

Sources

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