Developable surface: Difference between revisions
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* It is a [[ruled surface]] | * It is a [[ruled surface]] | ||
* Its [[Gaussian curvature]] is everywhere zero | * 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== | ==External links== | ||
Latest revision as of 19:38, 18 May 2008
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 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.