helicoid

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helicoid

[′hel·ə‚kȯid]
(invertebrate zoology)
Of a gastropod shell, shaped like a flat coil or flattened spiral.
(mathematics)
A surface generated by a curve which is rotated about a straight line and also is translated in the direction of the line at a rate that is a constant multiple of its rate of rotation.
References in periodicals archive ?
The cylindrical worm having the flanks as helical surfaces of the type involute helicoid is named involute worm or E worm.
The cylindrical worm having the flanks helical surfaces of the type of Archimedes helicoid is named Archimedes worm or A worm.
Mathematicians can also imagine twisting that plane to produce another infinite shape called the helicoid.
For centuries, the plane and the helicoid were the only known examples of infinite, unbounded minimal surfaces that don't fold back to intersect themselves.
Although computer images and other evidence strongly suggested that the new surface met the criteria for placing it, alongside the helicoid and the plane, in the minimal-surface hall of fame, that wasn't enough for mathematicians.
15 Proceedings of the National Academy of Sciences, establishes that a particular shape--a helicoid with a handle--doesn't intersect itself.
Twisting the ordinary two-dimensional plane into a helicoid converts the plane's flatness into saddle-based curviness.
In the early 1990s, David Hoffman and Fusheng Wei, then at the University of Massachusetts at Amherst, and Hermann Karcher of the University of Bonn in Germany discovered complicated equations that seemed to represent a surface just like the helicoid but with a tunnel penetrating one of the levels.