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Circled helicoid

Torse column, coil, and Saint-Gilles screw (by Robert March)

Other name: cyclic helicoid.

Cartesian parametrization:  where  is the parametrization of the circle a diameter of which lies on Ox, with center (a, 0, 0), radius b, forming an angle  with the horizontal.
We get the Saint-Gilles screw for  the torse column for  and the coil for .

The circled helicoids are the helicoids generated by the helicoidal movement of a circle.

Three remarkable positions of the generating circle can be distinguished:

Saint Gilles screw: vertical generating circle (in a plane containing the axis).
Torse column: horizontal generating circle (perpendicular to the axis).
Coil: generating circle perpendicular to the central helix.

The Saint Gilles screw in the case where the axis of the helicoid is a diameter of the circle ( and ) is called by [Gray] "corkscrew surface" or "twisted sphere"; its parametrization is: .

See also "helihorns".

The original Saint Gilles screw, near Arles

Model made by Robert March
The vault of this helicoidal staircase is half a Saint-Gilles screw.


The torse columns (?) of the altar of St. Peter's Basilica in the Vatican

Triple torse column

The serpentine column at Istanbul; to what family does it belong???

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© Robert FERRÉOL  2017