Friday, January 29, 2016

[fajnpdpd] Biquadratic surfaces

Investigate quadratic surfaces of (u, v, w) = (x^2, y^2, z^2), equivalently quartic surfaces of even degree.

Included in this family is the torus.

What is the relationship between one of these biquadratic surfaces and its "square root", a quadratic surface?

Inspired by: the conic sections, i.e., the quadratic curves in 2 dimensions, cover all the aesthetically simple curves in 2D.  But the quadrics seem not to in 3D, missing things like the torus, which seem simple enough.

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