Republic of Mathematics blog

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 (x^2 + frac{9y^2}{4} + z^2 - 1)^3 = x^2z^3 + frac{y^2z^3}{9} defines a set of points in xyz space that forms a lovely surface, hospital dear to the (x^2 + frac{9y^2}{4} + z^2 - 1)^3 = x^2z^3 + frac{y^2z^3}{9} 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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