Conoid
Ruled surface made of lines parallel to a plane and intersecting an axis / From Wikipedia, the free encyclopedia
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In geometry a conoid (from Greek κωνος 'cone' and -ειδης 'similar') is a ruled surface, whose rulings (lines) fulfill the additional conditions:
- (1) All rulings are parallel to a plane, the directrix plane.
- (2) All rulings intersect a fixed line, the axis.
The conoid is a right conoid if its axis is perpendicular to its directrix plane. Hence all rulings are perpendicular to the axis.
Because of (1) any conoid is a Catalan surface and can be represented parametrically by
Any curve x(u0,v) with fixed parameter u = u0 is a ruling, c(u) describes the directrix and the vectors r(u) are all parallel to the directrix plane. The planarity of the vectors r(u) can be represented by
- .
If the directrix is a circle, the conoid is called a circular conoid.
The term conoid was already used by Archimedes in his treatise On Conoids and Spheroides.