Doubly ruled surface

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This article defines a property that makes sense for a surface embedded in \R^3, 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 \R^3 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 z = 0 (the xy-plane)
circular hyperboloid of one sheet \frac{x^2}{a^2} + \frac{y^2}{a^2} - \frac{z^2}{c^2} = 1
hyperbolic paraboloid z = \frac{y^2}{b^2} - \frac{x^2}{a^2}

Relation with other properties

Weaker properties