Channel surface: Difference between revisions

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A channel or canal surface is a surface formed as the envelope of a family of spheres whose centers lie on a space curve. One sheet of the focal surface of a channel surface will be the generating curve.

A surface of revolution is a channel surface whose centers lie on a straight line. Dupin cyclides form a special class of surfaces which are channel surfaces in two distinct ways: for cyclides both sheets of the focal surface are curves; in fact they are both conic sections.

References

Hilbert, David; Cohn-Vossen, Stephan (1952). Geometry and the Imagination (2nd ed. ed.). Chelsea. p. 219. ISBN 0-8284-1087-9. {{cite book}}: |edition= has extra text (help)CS1 maint: multiple names: authors list (link)

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 A '''channel''' or '''canal surface''' is a [[surface]] formed as the [[envelope (mathematics)|envelope]] of a family of [[sphere]]s whose centers lie on a [[space curve]]. One sheet of the [[focal surface]] of a channel surface will be the generating curve.
-A [[surface of revolution]] is a channel surface whose centers lie on a straight line. [[Cyclide|Dupin cyclide]]s form a special class of surfaces which are channel surfaces in two distinct ways: for cyclides both sheets of the [[focal surface]] are curves; in fact they are both [[conic section|conics section]]s.
+A [[surface of revolution]] is a channel surface whose centers lie on a straight line. [[Cyclide|Dupin cyclide]]s form a special class of surfaces which are channel surfaces in two distinct ways: for cyclides both sheets of the [[focal surface]] are curves; in fact they are both [[conic section]]s.
 ==References==