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.
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 ...
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.
A hyperboloid of two sheets A torus A helicoid. Simple examples. A simple example of a regular surface is given by the 2-sphere {(x, y, z) | x 2 + y 2 + z 2 = 1}; this surface can be covered by six Monge patches (two of each of the three types given above), taking h(u, v) = ± (1 − u 2 − v 2) 1/2.
Animation showing the deformation of a helicoid into a catenoid as θ changes.. In differential geometry, the associate family (or Bonnet family) of a minimal surface is a one-parameter family of minimal surfaces which share the same Weierstrass data.
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.
For premium support please call: 800-290-4726 more ways to reach us
The pitch of a helix is the height of one complete helix turn, measured parallel to the axis of the helix.. A double helix consists of two (typically congruent) helices with the same axis, differing by a translation along the axis.