What do these equations represent? What are X, Y, and Z ? —Dan ----- For the (3,4) knot I calculated that, 0 = -81 X^2 + 117 X^4 - 40 X^6 + 4 X^8 - 81 Y^2 + 234 X^2 Y^2 - 152 X^4 Y^2 + 16 X^6 Y^2 + 117 Y^4 - 152 X^2 Y^4 + 24 X^4 Y^4 - 40 Y^6 + 16 X^2 Y^6 + 4 Y^8 0 = 9 X^2 - 9 X^4 + 9 Y^2 + 14 X^2 Y^2 - 9 Y^4 - 144 Z^2 + 64 X^2 Z^2 + 64 Y^2 Z^2 {X,Y,Z} = {Sin[t] + 2 Sin[3 t], Cos[t] - 2 Cos[3 t], Sin[4 t]} . The total number of (X,Y) monomials increases quadratically and total (X,Y,Z) monomials increase cubically, as functions of degree. These equations can be solved to give an upper degree bound. For integral calculations, this is a really nice way to represent the knot. We already have a [0,2*pi] parameterization built in, and trigonometric polynomials are easy to integrate. Nice Idea! -----