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In the mathematical area of knot theory, a Reidemeister move is any of three local moves on a link diagram. Kurt Reidemeister () and, independently, James Waddell Alexander and Garland Baird Briggs (), demonstrated that two knot diagrams belonging to the same knot, up to planar isotopy, can be related by a sequence of the three Reidemeister moves.
It will hold fast when loaded, but slip when shock loaded until tension is relieved enough for it to again hold fast. It serves the same purpose as the taut-line hitch, e.g. tensioning a tent's guy line. This knot is also called the adjustable loop [1] and Cawley adjustable hitch. It was conceived 1982 by Canadian climber Robert Chisnall.
Shock polar in the pressure ratio-flow deflection angle plane for a Mach number of 1.8 and a specific heat ratio 1.4. The minimum angle, , which an oblique shock can have is the Mach angle = (/), where is the initial Mach number before the shock and the greatest angle corresponds to a normal shock.
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 {\displaystyle n} , then there exists a diagram of the knot which can be changed to unknot by switching n {\displaystyle n} crossings. [ 1 ]
More precisely, if K is a smooth knot, then for almost every unit vector v giving the direction, orthogonal projection onto the plane perpendicular to v gives a knot diagram, and we can compute the crossing number, denoted n(v). The average crossing number is then defined as the integral over the unit sphere: [1]
Any framed knot has a self-linking number obtained by computing the linking number of the knot C with a new curve obtained by slightly moving the points of C along the framing vectors. The self-linking number obtained by moving vertically (along the blackboard framing) is known as Kauffman's self-linking number.
A reduced diagram is one in which all the isthmi are removed. Tait came up with his conjectures after his attempt to tabulate all knots in the late 19th century. As a founder of the field of knot theory, his work lacks a mathematically rigorous framework, and it is unclear whether he intended the conjectures to apply to all knots, or just to alternating knots.
Diagram showing the (theoretical) 3:1 mechanical advantage of the Trucker's Hitch. In tightening the trucker's hitch, tension can be effectively increased by repeatedly pulling sideways while preventing the tail end from slipping through the loop, and then cinching the knot tighter as the sideways force is released. This is called "sweating a ...