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## Main Question or Discussion Point

Greetings,

I am trying to figure out how to modify the equations for a trefoil knot to make it toroidal.

A trefoil knot is:

x = (2 + cos 3t)cos 2t

y = (2 + cos 3t)sin 2t

z = sin 3t

A torus is:

x(u, v) = (R + r cos v) cos u

y(u, v) = (R + r cos v) sin u

z(u,v) = r sin v

where

u, v are in the interval [0, 2π),

R is the distance from the center of the tube to the center of the torus,

r is the radius of the tube.

Thanks

I am trying to figure out how to modify the equations for a trefoil knot to make it toroidal.

A trefoil knot is:

x = (2 + cos 3t)cos 2t

y = (2 + cos 3t)sin 2t

z = sin 3t

A torus is:

x(u, v) = (R + r cos v) cos u

y(u, v) = (R + r cos v) sin u

z(u,v) = r sin v

where

u, v are in the interval [0, 2π),

R is the distance from the center of the tube to the center of the torus,

r is the radius of the tube.

Thanks