Developable surface

This article defines a property that makes sense for a surface embedded in

${\mathbb{R}}^3$

, 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 ${\mathbb{R}}^3$ is termed developable if it satisfies both these conditions:

• It is a ruled surface
• Its Gaussian curvature is everywhere zero, viz it is a flat surface

Equivalently, a surface is developable if it can be generated by a one-parameter family of lines.

Relation with other properties

Stronger properties

• Tangent-developable surface

Weaker properties

• Ruled surface
• Flat surface

External links

Definition links

• Mathworld page