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Homedevelopable surface

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# developable surface

A generatrix of a ruled surface is torsal, if in each of its points there is one and the same tangent plane of the surface.

A ruled surface is torsal iff it only has torsal generatrices.

A surface is developable, if one can spread it out on a plane without any stretching or tearing.

K. F. Gauss has proved that a surface is developable if and only if it is a torsal ruled surface.

One may divide the developable surfaces into three types:

1. 2. 3. Tangential surfaces of a space curve; they can be expressed by

$\vec{r}=\vec{\gamma}(t)+s\,\frac{d\vec{\gamma}(t)}{dt}$ where $\vec{r}=\vec{\gamma}(t)$ is the equation of the space curve, $s$ and $t$ are parameters.

Defines:

developable, torsal generatrix, torsal, tangential surface

Related:

Area2, RiemannMultipleIntegral

Synonym:

torsal surface

Type of Math Object:

Topic

Major Section:

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Parent:

Groups audience:

## Mathematics Subject Classification

51M20*no label found*51M04

*no label found*

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