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A helicoid with α = 1, −1 ≤ ρ ≤ 1 and − π ≤ θ ≤ π. The helicoid , also known as helical surface , is a smooth surface embedded in three-dimensional space . It is the surface traced by an infinite line that is simultaneously being rotated and lifted along its fixed axis of rotation.
generalized helicoid: meridian is a parabola. In geometry, a generalized helicoid is a surface in Euclidean space generated by rotating and simultaneously displacing a curve, the profile curve, along a line, its axis. Any point of the given curve is the starting point of a circular helix.
In fluid dynamics, an isotropic helicoid is a shape that is helical, so it rotates as it moves through a fluid, and yet is isotropic, so that its rotation and drag are the same for all orientations of the particle.
The geometric shape of the directrices and generators are of course essential to the shape of the ruled surface they produce. ... The helicoid is a special case of ...
A helix (/ ˈ h iː l ɪ k s /; pl. helices) is a shape like a cylindrical coil spring or the thread of a machine screw. It is a type of smooth space curve with tangent lines at a constant angle to a fixed axis.
The differential dn of the Gauss map n can be used to define a type of extrinsic curvature, known as the shape operator [55] or Weingarten map. This operator first appeared implicitly in the work of Wilhelm Blaschke and later explicitly in a treatise by Burali-Forti and Burgati. [ 56 ]
The helicoid is a ruled surface – but unlike the ruled surfaces mentioned above, it is not a developable surface. The hyperbolic paraboloid and the hyperboloid are slightly different doubly ruled surfaces – but unlike the ruled surfaces mentioned above, neither one is a developable surface.
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