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Space curves and knots112 of 113

Trefoil knot

Peter Guthrie Tait, 1885

Tie an overhand knot in a cord and join the two ends, and the loop is a trefoil, the simplest knot that cannot be undone without cutting. It is the only knot that needs exactly three crossings to draw. It comes in two forms, each the mirror image of the other, and no movement in space turns one into the other. It is also the edge of a band given three half-twists.

(sin t + 2 sin 2t, cos t - 2 cos 2t, -sin 3t)

On mathcurve.com as Nœud de trèfle

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