# What type of curve is $\left|\dfrac{x}{a}\right|^{z} + \left|\dfrac{y}{b}\right|^{z} = 1$?

In order to fit experimental data, I want to use a Cartesian equation which looks like:

$\left|\dfrac{x}{a}\right|^{z} + \left|\dfrac{y}{b}\right|^{z} = 1$

$a$, $b$, $c$, and $z$ can take any real value, except the impossible ones ($a = 0$ or $b = 0$, for instance).

First, I look for a name for this equation because I can't find more information about it if I can't name it. As far as I know, ellipsoids, paraboloids, or hyperboloids are not helpful here, since with those specific cases, $z = 2$, and that's all.

Any idea? Thanks!

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Superellipse / Lamé curve (Wikipedia / Mathworld):

$\hskip 2.1 in$

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Great! It definitely looks like the shape I'm looking for and I now know the name associated with the equation. Thanks a lot! – Speredenn Jul 24 '11 at 15:48

It's referred to as a Lamé curve or a superellipse.

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Here is another nice page on these... – J. M. Jul 24 '11 at 15:24
Thanks for the links and for the edit :-) – Speredenn Jul 24 '11 at 16:17