# I (x^2 + 9y^2/4 + z^2 – 1)^3 == x^2z^3 + y^2z^3/9 math

Posted by: Gary Ernest Davis on: April 3, 2011

The equation defines a set of points in space that forms a lovely surface, hospital dear to the of all mathematicians:

*Mathematica* code

The image above was produced using *Mathematica*.

Here is the (one line) code:

**ContourPlot3D[(x^2 + 9*y^2/4 + z^2 – 1)^3 == ****x^2*z^3 + y^2*z^3/9, {x, -3/2, 3/2}, {y, -3/2, 3/2}, {z, -3/2, 3/2},**** Mesh -> None, Boxed -> False, Axes -> False, ****ContourStyle -> Directive[Red, Opacity[0.8], Specularity[White, 30]]]**

x

One can also get a mesh version (not in red) from Wolfram Alpha using the entry

**ContourPlot3D[(x^2 + 9*y^2/4 + z^2 – 1)^3 == ****x^2*z^3 + y^2*z^3/9, {x, -3/2, 3/2}, {y, -3/2, 3/2}, {z, -3/2, 3/2}]**

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