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.