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Ruled surface
In
geometry
, a
surface
S
is
ruled
(also called a
scroll
) if through every point of
S
there is a straight line that lies on
S
. The most familiar examples (illustrated here in three-dimensional
Euclidean space
) are the
plane
and the curved surface of a
cylinder
or
cone
. Other examples are a
conical surface
with
elliptical
directrix
, the
right conoid
, the
helicoid
, and the
tangent developable
of a smooth
curve
in space.
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