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Cartesian Lemniscate
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https://preview.redd.it/db4ktu77nrg61.png?width=800&format=png&auto=webp&s=e1acaf43a213484fc9396e27f31f870da46652de

I have been trying to figure out how to graph a lemniscate using only a rectangular equation for some time. This morning, I was working on something when I just stumbled upon this.

The equation is:

0 = x^4 x^2 * y^2 - 25x^2 25y^2

https://www.desmos.com/calculator/vq8ph9ohxm

Does anybody know how it makes the shape that it does? I'm just trying to break the equation down so I understand better.

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3 years ago