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In knot theory, the writhe is a property of an oriented link diagram. The writhe is the total number of positive crossings minus the total number of negative crossings. A direction is assigned to the link at a point in each component and this direction is followed all the way around each component. For each crossing one comes across while traveling in this direction, if the strand un
Later knot tables took two approaches to resolving this: some just skipped one of the entries without renumbering, and others renumbered the later entries to remove the hole. The resulting ambiguity has continued to the present day, and has been further compounded by mistaken attempts to correct errors caused by this that were themselves incorrect.
7 4 knot, "endless knot" 8 18 knot, "carrick mat" 10 161 /10 162, known as the Perko pair; this was a single knot listed twice in Dale Rolfsen's knot table; the duplication was discovered by Kenneth Perko; 12n242/(−2,3,7) pretzel knot (p, q)-torus knot - a special kind of knot that lies on the surface of an unknotted torus in R 3
KnotInfo: Table of Knot Invariants and Knot Theory Resources; The Knot Atlas — detailed info on individual knots in knot tables; KnotPlot — software to investigate geometric properties of knots; Knotscape — software to create images of knots; Knoutilus — online database and image generator of knots
The unknotting number of a knot is always less than half of its crossing number. [2] This invariant was first defined by Hilmar Wendt in 1936. [3] 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:
Static attribute tables contain two columns, one for the identity of the entity to which the value belongs and one for the actual property value. Historized attribute tables have an extra column for storing the starting point of a time interval. In a knotted attribute table, the value column is an identity that references a knot table.
The projection then gives us a tangle diagram, where we make note of over and undercrossings as with knot diagrams. Tangles often show up as tangle diagrams in knot or link diagrams and can be used as building blocks for link diagrams, e.g. pretzel links.
In 1637 Descartes was the first to unite the German radical sign √ with the vinculum to create the radical symbol in common use today. [8] The symbol used to indicate a vinculum need not be a line segment (overline or underline); sometimes braces can be used (pointing either up or down). [9]