Astroidal ellipsoid
Surfaces
Description
The Astroidal ellipsoid is a three-dimensional surface which is the inverse of the ellipsoid in the sense that it "goes in" where the ellipsoid "goes out."
References
Object definitions
Mapping
- TeX
- MathML
- Mathematica input
- Maple input
\left\{x\to a \cos ^3(u) \cos ^3(v),y\to b \sin ^3(u) \cos ^3(v),z\to c \sin ^3(v)\right\}
<math>
<mrow>
<mo>{</mo>
<mrow>
<mrow>
<mi>x</mi>
<semantics>
<mo>→</mo>
<annotation encoding='Mathematica'>"\[Rule]"</annotation>
</semantics>
<mrow>
<mi>a</mi>
<mo>⁢</mo>
<mrow>
<msup>
<mi>cos</mi>
<mn>3</mn>
</msup>
<mo>(</mo>
<mi>u</mi>
<mo>)</mo>
</mrow>
<mo>⁢</mo>
<mrow>
<msup>
<mi>cos</mi>
<mn>3</mn>
</msup>
<mo>(</mo>
<mi>v</mi>
<mo>)</mo>
</mrow>
</mrow>
</mrow>
<mo>,</mo>
<mrow>
<mi>y</mi>
<semantics>
<mo>→</mo>
<annotation encoding='Mathematica'>"\[Rule]"</annotation>
</semantics>
<mrow>
<mi>b</mi>
<mo>⁢</mo>
<mrow>
<msup>
<mi>sin</mi>
<mn>3</mn>
</msup>
<mo>(</mo>
<mi>u</mi>
<mo>)</mo>
</mrow>
<mo>⁢</mo>
<mrow>
<msup>
<mi>cos</mi>
<mn>3</mn>
</msup>
<mo>(</mo>
<mi>v</mi>
<mo>)</mo>
</mrow>
</mrow>
</mrow>
<mo>,</mo>
<mrow>
<mi>z</mi>
<semantics>
<mo>→</mo>
<annotation encoding='Mathematica'>"\[Rule]"</annotation>
</semantics>
<mrow>
<mi>c</mi>
<mo>⁢</mo>
<mrow>
<msup>
<mi>sin</mi>
<mn>3</mn>
</msup>
<mo>(</mo>
<mi>v</mi>
<mo>)</mo>
</mrow>
</mrow>
</mrow>
</mrow>
<mo>}</mo>
</mrow>
</math>
{x -> a*Cos[u]^3*Cos[v]^3, y -> b*Cos[v]^3*Sin[u]^3, z -> c*Sin[v]^3}
[x = a*cos(u)^3*cos(v)^3, y = b*cos(v)^3*sin(u)^3, z = c*sin(v)^3]
Constants
- TeX
- MathML
- Mathematica input
- Maple input
\{a,b,c\}
<math>
<mrow>
<mo>{</mo>
<mrow>
<mi>a</mi>
<mo>,</mo>
<mi>b</mi>
<mo>,</mo>
<mi>c</mi>
</mrow>
<mo>}</mo>
</mrow>
</math>
{a, b, c}
[a, b, c]
Cite this as:
Surfaces: Astroidal ellipsoid from Differential Geometry Library. http://digi-area.com/DifferentialGeometryLibrary/Surfaces/Astroidal-Ellipsoid.php
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