Portal:Geometry/Selected picture
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The above shows an example of doubly ruled surface - the hyperboloid of one sheet. Although the wires are straight lines, they are lying within the surface. Through any point on this surface pass two straight lines, so it is doubly ruled.
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One of way on constructing an astroid, by tracking the path a point on the smaller circle follows as it rolled round within the larger cricle. Hence, an astroid is a hypocycloid.
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