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How do you derive the parametric equations for a sphere? \begin{align} x & = r \cos(\theta)\sin(\varphi), \\ y & = r \sin(\theta)\sin(\varphi), \\ z & = r \cos(\varphi), \end{align} where $\theta$ is from $0$ to $2\pi$ and $\varphi$ is from $0$ to $\pi$. There are no good explanations online.

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    What about [$x^2+y^2+z^2 = 1$](http://www.wolframalpha.com/input/?i=z^2%2By^2%2Bx^2%3D1)?2012-05-28
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    http://en.wikipedia.org/wiki/Spherical_coordinate_system2012-05-30

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