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: right-handed coil, h = 0: torus, h < 0: left-handed 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.
 
 

Coil of a still

 
 

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© Robert FERRÉOL  2017