Search results
Results from the WOW.Com Content Network
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.
Helicoid as translation surface with identical generatrices , Helicoid as translation surface: any parametric curve is a shifted copy of the purple helix. A helicoid is a special case of a generalized helicoid and a ruled surface. It is an example of a minimal surface and can be represented as a translation surface. The helicoid with the ...
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.
Examples include the plane, the lateral surface of a cylinder or cone, a conical surface with elliptical directrix, the right conoid, the helicoid, and the tangent developable of a smooth curve in space. A ruled surface can be described as the set of points swept by a moving straight line.
This leads to an infinite cyclic monodromy group and a covering of {} by a helicoid (an example of a Riemann surface). In mathematics, monodromy is the study of how objects from mathematical analysis, algebraic topology, algebraic geometry and differential geometry behave as they "run round" a singularity.
For premium support please call: 800-290-4726 more ways to reach us
Because they are members of the same associate family of surfaces, one can bend a catenoid into a portion of a helicoid without stretching. In other words, one can make a (mostly) continuous and isometric deformation of a catenoid to a portion of the helicoid such that every member of the deformation family is minimal (having a mean curvature of