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.
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.
The principles of hydraulics are used in a crosshead die that employs a helicoid
or a distribution system.
For centuries, the helicoid has been the only known example of a so-called "complete embedded minimal surface of finite topology with infinite total curvature.
This feature, which looks like a hole in the fundamental helicoid shape, makes the new surface topologically equivalent to a punctured sphere equipped with a handle -- just like the one that sprouts from a mug.
Van de Woestyne, A new characterization of the helicoids
, Geometry and Topology of Submanifolds V.
n+1] , and helicoids
of the 1st, 2nd, and 3rd kind, conjugate Enneper's surfaces of the second kind, and B-scrolls in [E.
Among the topics covered are computational aspects of discrete minimal surfaces, conjugate plateau constructions, parabolicity and minimal surfaces, the isoperimetric problem, the genus-one helicoids
as a limit of screw-motion invariant helicoids
with handles, isoperimetric inequalities of minimal submanifolds, embedded minimal disks, minimial surfaces of finite topology, conformal structures and necksizes of embedded constant mean curvature surfaces, and variational problems in Lagrangian geometry.
spheres, hollow helicoids
and soft lithographically defined micron scale patterns of new classes of nanomaterials having crystalline mesoporosity using supramolecular templates and summarized in their paper 'Curves in Chemistry -- Supramolecular Materials Taking Shape', Canadian Journal of Chemistry.
The external helicoids of the cone screw and the internal helicoids of the bush form a series of seal cavities, and the seal cavities go over the discharge end by spiral with the rotation of the cone screw.
The internal surface of the shell and the internal and external surface of the bush about the new pump are both the double line helicoids, the internal surface of the bush is shown as the Figs.
The lamellar profiles (S or C) can, according to these authors, result from slices that are at oblique angles (not parallel to ) through helicoids
with straight profiles (from a view along ).
The analysis of the graphs shows that this parameter has a very significant influence, because its increase generates helicoids
furrows the result of tool shape and helicoids