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 :
 1.
 2.

3.
Tangential surfaces of a space curve^{}; they can be expressed by
$$\overrightarrow{r}=\overrightarrow{\gamma}(t)+s\frac{d\overrightarrow{\gamma}(t)}{dt}$$ where $\overrightarrow{r}=\overrightarrow{\gamma}(t)$ is the equation of the space curve, $s$ and $t$ are parameters.
Title  developable surface 
Canonical name  DevelopableSurface 
Date of creation  20130322 15:29:29 
Last modified on  20130322 15:29:29 
Owner  pahio (2872) 
Last modified by  pahio (2872) 
Numerical id  8 
Author  pahio (2872) 
Entry type  Topic 
Classification  msc 51M20 
Classification  msc 51M04 
Synonym  torsal surface 
Related topic  Area2 
Related topic  RiemannMultipleIntegral 
Defines  developable 
Defines  torsal generatrix 
Defines  torsal 
Defines  tangential surface 