Category:Definitions/Parallel Surfaces

This category contains definitions related to Parallel Surfaces.
Related results can be found in Category:Parallel Surfaces.

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.