Mathematical knots come from a branch of mathematics called knot theory, which studies knots as pure shapes rather than as tools. Here a knot is a closed loop with its ends joined together, so it can be stretched, twisted, and bent freely, but never untied. Mathematicians ask when two tangled loops are really the same knot in disguise and when they are genuinely different. The simplest example that cannot be untangled into a plain circle is the Trefoil Knot, which crosses over itself just three times. The Trefoil Knot is also chiral, meaning it and its mirror image can never be bent into each other, a distinction that matters well beyond mathematics, since molecules and even strands of DNA can be knotted in the same way.
Warning
Verify tying technique with a skilled instructor where knot failure could cause property damage, injury, or death.
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