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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.
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 ...
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.
A helicoid minimal surface formed by a soap film on a helical frame. In mathematics, a minimal surface is a surface that locally minimizes its area. This is equivalent to having zero mean curvature (see definitions below).
Ruled surface generated by two Bézier curves as directrices (red, green). A surface in 3-dimensional Euclidean space is called a ruled surface if it is the union of a differentiable one-parameter family of lines.
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Sympodial growth patterns in a flowerhead: helicoid (left) and scorpioid (right) cymes, side and top views Laelia superbiens , a sympodial orchid. In botany , sympodial growth is a bifurcating branching pattern where one branch develops more strongly than the other, resulting in the stronger branches forming the primary shoot and the weaker ...