The Twisted Cubic The curve parameterized by (t,t^2,t^3) in affine 3 space viewed as the intersection of the two hypersurfaces z=x^3, y^2=x*z. If we consider affine 3 space as the set of real monic cubic polynomials, then this curve is equivalent to the set of cubes of linear polynomials. This affine twisted cubic can also be described as the common zeros of the quadrics y-x^2 and z-xy.
The Twisted Cubic The curve parameterized by (t,t^2,t^3) in affine 3 space viewed as the intersection of the two hypersurfaces z=x^3, y^2=x*z. If we consider affine 3 space as the set of real monic cubic polynomials, then this curve is equivalent to the set of cubes of linear polynomials. This affine twisted cubic can also be described as the common zeros of the quadrics y-x^2 and z-xy.
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