# Doubly ruled surface

From Diffgeom

This article defines a property that makes sense for a surface embedded in , viz three-dimensional Euclidean space. The property is invariant under orthogonal transformations and scaling, i.e., under all similarity transformations.

View other such properties

## Definition

A surface embedded in is said to be **doubly ruled** if given any point in the surface, there are two distinct lines through the point, that lie completely on the surface.

## Classification

`Further information: Classification of doubly ruled surfaces`

Doubly ruled surface | Equational/implicit description |
---|---|

Euclidean plane | (the -plane) |

circular hyperboloid of one sheet | |

hyperbolic paraboloid |