Pluckers conoid
Surfaces
Description
The Plucker's conoid is a ruled surface named after the German mathematician Julius Plucker. It is also called a cylindroid (a cylinder that has an elliptical cross-section) or conical wedge.
References
Object definitions
Mapping
- TeX
- MathML
- Mathematica input
- Maple input
\{x\to v \cos (u),y\to v \sin (u),z\to a \sin (n u)\}
<math>
<mrow>
<mo>{</mo>
<mrow>
<mrow>
<mi>x</mi>
<semantics>
<mo>→</mo>
<annotation encoding='Mathematica'>"\[Rule]"</annotation>
</semantics>
<mrow>
<mi>v</mi>
<mo>⁢</mo>
<mrow>
<mi>cos</mi>
<mo>⁡</mo>
<mo>(</mo>
<mi>u</mi>
<mo>)</mo>
</mrow>
</mrow>
</mrow>
<mo>,</mo>
<mrow>
<mi>y</mi>
<semantics>
<mo>→</mo>
<annotation encoding='Mathematica'>"\[Rule]"</annotation>
</semantics>
<mrow>
<mi>v</mi>
<mo>⁢</mo>
<mrow>
<mi>sin</mi>
<mo>⁡</mo>
<mo>(</mo>
<mi>u</mi>
<mo>)</mo>
</mrow>
</mrow>
</mrow>
<mo>,</mo>
<mrow>
<mi>z</mi>
<semantics>
<mo>→</mo>
<annotation encoding='Mathematica'>"\[Rule]"</annotation>
</semantics>
<mrow>
<mi>a</mi>
<mo>⁢</mo>
<mrow>
<mi>sin</mi>
<mo>⁡</mo>
<mo>(</mo>
<mrow>
<mi>n</mi>
<mo>⁢</mo>
<mi>u</mi>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
</mrow>
</mrow>
<mo>}</mo>
</mrow>
</math>
{x -> v*Cos[u], y -> v*Sin[u], z -> a*Sin[n*u]}
[x = v*cos(u), y = v*sin(u), z = a*sin(n*u)]
Constants
- TeX
- MathML
- Mathematica input
- Maple input
\{a,n\}
<math>
<mrow>
<mo>{</mo>
<mrow>
<mi>a</mi>
<mo>,</mo>
<mi>n</mi>
</mrow>
<mo>}</mo>
</mrow>
</math>
{a, n}
[a, n]
Cite this as:
Surfaces: Pluckers conoid from Differential Geometry Library. http://digi-area.com/DifferentialGeometryLibrary/Surfaces/Pluckers-Conoid.php
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