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In knot theory, a chord diagram can be used to describe the sequence of crossings along the planar projection of a knot, with each point at which a crossing occurs paired with the point that crosses it. To fully describe the knot, the diagram should be annotated with an extra bit of information for each pair, indicating which point crosses over ...
In the mathematical field of knot theory, Fox n-coloring is a method of specifying a representation of a knot group or a group of a link (not to be confused with a link group) onto the dihedral group of order n where n is an odd integer by coloring arcs in a link diagram (the representation itself is also often called a Fox n-coloring).
Urban Dictionary Screenshot Screenshot of Urban Dictionary front page (2018) Type of site Dictionary Available in English Owner Aaron Peckham Created by Aaron Peckham URL urbandictionary.com Launched December 9, 1999 ; 25 years ago (1999-12-09) Current status Active Urban Dictionary is a crowdsourced English-language online dictionary for slang words and phrases. The website was founded in ...
Knots can be described in various ways. Using different description methods, there may be more than one description of the same knot. For example, a common method of describing a knot is a planar diagram called a knot diagram, in which any knot can be drawn in many different ways.
A tricolored trefoil knot. In the mathematical field of knot theory, the tricolorability of a knot is the ability of a knot to be colored with three colors subject to certain rules. Tricolorability is an isotopy invariant, and hence can be used to distinguish between two different (non-isotopic) knots.
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]
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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