Ruled Surfaces
In geometry, a Differential geometry of surfaces, surface in 3-dimensional Euclidean space is ruled (also called a scroll) if through every Point (geometry), point of , there is a straight line that lies on . Examples include the plane (mathematics), plane, the lateral surface of a cylinder (geometry), cylinder or cone (geometry), cone, a conical surface with ellipse, elliptical directrix (rational normal scroll), directrix, the right conoid, the helicoid, and the tangent developable of a smooth curve in space. A ruled surface can be described as the set of points swept by a moving straight line. For example, a cone is formed by keeping one point of a line fixed whilst moving another point along a circle. A surface is doubly ruled if through every one of its points there are two distinct lines that lie on the surface. The hyperbolic paraboloid and the hyperboloid of one sheet are doubly ruled surfaces. The plane is the only surface which contains at least three distinct lines thr ...
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