Hello guys, at the link(adsbygoogle = window.adsbygoogle || []).push({});

http://mathworld.wolfram.com/Superellipse.html

you can find the definition of superellipse. Now consider the particular super ellipse

[tex]\frac{x^{2n}}{A^{2n}} +\frac{y^{2n}}{B^{2n}} = 1 [/tex]

In which A,B, are constant and n is a positive integer.

What is the coordinate system that has two families of curves in which one represents the superellipse and the other one is perpendicular to it? In the particular case of A = B, n = 1, the coordinate system is

[tex]x = r\cos{\varphi}[/tex]

[tex]y = r\sin{\varphi}[/tex]

If A is different than B but still n =1, the coordinate system is similar but it involves also hyperbolic sine and cosine and one family of curves is the generic ellipse and the other family is the generic hyperbola and they are perpendicular to each other, like it happens in the polar coordinates. So, is there a similar curvilinear coordinate system for the particular superellipse I described?

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# Superellipse and a good coordinate system

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