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COIL
Other names: helical tube, spring, toroidal helicoid. 
Cartesian parametrization: , where b is the radius of the tube, a the distance from the central helix to the axis, and 2ph the shift of this helix and therefore h/a its slope.
h > 0: righthanded coil, h = 0: torus, h < 0: lefthanded coil. 
The coils are the tubes the bore of which are circular helices.
They are the helicoids the directrix of which is a circle perpendicular to the speed vector of the helical motion; see at circled helicoid.



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© Robert FERRÉOL 2017