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, viz it is a [[flat 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==
==Relation with other properties==

Revision as of 15:48, 6 July 2007

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

R3

, 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 R3 is termed developable if it satisfies both these conditions:

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

Relation with other properties

Stronger properties

Weaker properties

External links

Definition links