Curves

For some curves r(t)=(x(t),y(t)) in the plane, one can eliminate the parameter t, like for example in the case r(t)=(cos(t),sin(t)), using cos22(t)+sin2(t)=1. If we eliminate the parameter for a three dimensional curve r(t)=(x(t),y(t),z(t)), we end up with two equations. Geometricially, the curve is then the intersection of two surfaces. For example, the spiral curve r(t)=(cos(t),sin(t),t) is the intersection of the two surfaces x=cos(z), y=sin(z).