Helicoid - Wikipedia
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 -- from Wolfram MathWorld
The (circular) helicoid is the minimal surface having a (circular) helix as its boundary. It is the only ruled minimal surface other than the plane (Catalan 1842, do Carmo 1986). For many years, the helicoid remained the only known example of a complete embedded minimal surface of finite topology with infinite curvature.
Helicoid - Encyclopedia of Mathematics
2023年11月12日 · The equation of a helicoid in parametric form is \[ x = \rho \cos t \quad y = \rho \sin t \quad z = \rho \arctan \alpha + kt\, . \] If $\alpha = \pi/2$ the helicoid is called straight or right (cf. Fig. 1), otherwise it is called oblique.
Helicoid - Michigan State University
It is the only Ruled Minimal Surface other than the Plane (Catalan 1842, do Carmo 1986). For many years, the helicoid remained the only known example of a complete embedded Minimal Surface of finite topology with infinite Curvature.
Helicoid-Catenoid - Virtual Math Museum
The helicoid and catenoid are a family of minimal surfaces. Each surface in the family is isometric to any other, meaning, the length between any two points A and B of any curve on a surface, remain unchanged.
Helicoid Definition & Meaning - Merriam-Webster
The meaning of HELICOID is forming or arranged in a spiral. How to use helicoid in a sentence.
Generalized helicoid - Wikipedia
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 - (Metric Differential Geometry) - Vocab, Definition ...
A helicoid is a type of surface in three-dimensional space that can be described as a twisted plane, generated by moving a straight line along a helical path around a fixed axis. It possesses unique geometric properties, such as constant mean curvature and infinite torsion, making it an interesting object in differential geometry, especially ...
Helicoid - Scientific Lib
The helicoid, after the plane and the catenoid, is the third minimal surface to be known. Description. It was described by Euler in 1774 and by Jean Baptiste Meusnier in 1776. Its name derives from its similarity to the helix: for every point on the helicoid, there is a helix contained in the helicoid which passes through that point.
The Helicoid - Minimal Surfaces
Below is an animation showing the associate family from catenoid to helicoid, an isometric deformation. This deformation was first described by Heinrich Ferdinand Scherk around 1832, but not in the context of the associate family.