Unknotting Trefoil
Unknotting may refer to: *Unknotting number, the minimum number of times the knot must be passed through itself to untie it *Unknotting problem In mathematics, the unknotting problem is the problem of algorithmically recognizing the unknot, given some representation of a knot, e.g., a knot diagram. There are several types of unknotting algorithms. A major unresolved challenge is to d ...

Unknotting Number
In the mathematical area of knot theory, the unknotting number of a knot is the minimum number of times the knot must be passed through itself (crossing switch) to untie it. If a knot has unknotting number n, then there exists a diagram of the knot which can be changed to unknot by switching n crossings. The unknotting number of a knot is always less than half of its crossing number. Any composite knot has unknotting number at least two, and therefore every knot with unknotting number one is a prime knot. The following table show the unknotting numbers for the first few knots: Image:Blue Trefoil Knot.png, Trefoil knot unknotting number 1 Image:Blue Figure-Eight Knot.png, Figure-eight knot unknotting number 1 Image:Blue Cinquefoil Knot.png, Cinquefoil knot unknotting number 2 Image:Blue Three-Twist Knot.png, Three-twist knot unknotting number 1 Image:Blue Stevedore Knot.png, Stevedore knot unknotting number 1 Image:Blue 6_2 Knot.png, 6₂ knot unknotting number 1 Imag ...
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