A tangent developable of a curve 
is a ruled surface 
for which 
can be parameterized by 
. A tangent developable is a developable
surface.
For example, the circular helix
 |
where 
and 
,
generates the tangent developable
 |
where 
and 
range over the real numbers (Gray 1997). For fixed
,
varying 
traces the tangent line to the helix
at 
,
and setting 
recovers the helix. This surface
is distinct from the helicoid, whose rulings
are horizontal lines rather than tangent
lines to the helix.
