Category:Parallel Surfaces

This category contains results about Parallel Surfaces.
Definitions specific to this category can be found in Definitions/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.