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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 , then there exists a diagram of the knot which can be changed to unknot by switching 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 Image:Blue 6_3 Knot.png|6₃ knot unknotting number 1 Image:Blue 7_1 Knot.png|7₁ knot unknotting number 3 In general, it is relatively difficult to determine the unknotting number of a given knot. Known cases include: * The unknotting number of a nontrivial twist knot is always equal to one. * The unknotting number of a -torus knot is equal to . * The unknotting numbers of prime knots with nine or fewer crossings have all been determined. (The unknotting number of the 1011 prime knot is unknown.) ==Other numerical knot invariants== * Crossing number * Bridge number * Linking number * Stick number 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Unknotting number」の詳細全文を読む スポンサード リンク
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