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In topology, knot theory is the study of mathematical knots. While inspired by knots which appear in daily life, such as those in shoelaces and rope, a mathematical knot differs in that the ends are joined so it cannot be undone, the simplest knot being a ring (or " unknot ").
A polygonal knot is a knot whose image in R 3 is the union of a finite set of line segments. [6] A tame knot is any knot equivalent to a polygonal knot. [6] [Note 2] Knots which are not tame are called wild, [7] and can have pathological behavior. [7] In knot theory and 3-manifold theory, often the adjective "tame" is omitted. Smooth knots, for ...
Figure-eight knot (mathematics) the only 4-crossing knot; Granny knot (mathematics) and Square knot (mathematics) are a connected sum of two Trefoil knots; Perko pair, two entries in a knot table that were later shown to be identical. Stevedore knot (mathematics), a prime knot with crossing number 6; Three-twist knot is the twist knot with ...
4 1 knot/Figure-eight knot (mathematics) - a prime knot with a crossing number four; 5 1 knot/Cinquefoil knot, (5,2)-torus knot, Solomon's seal knot, pentafoil knot - a prime knot with crossing number five which can be arranged as a {5/2} star polygon ; 5 2 knot/Three-twist knot - the twist knot with three-half twists
In knot theory, prime knots are those ... 6 3 knot: 6 3: 6a1 4 8 10 2 12 6 [2112] ... List of mathematical knots and links; Knot tabulation (−2,3,7) pretzel knot; Notes
The Game of Trees is a Mad Math Theory That Is Impossible to Prove ... The Amazing Math Inside the Rubik’s Cube. Knot theorists’ holy grail problem was an algorithm to identify if some tangled ...
Figure-eight knot of practical knot-tying, with ends joined. In knot theory, a figure-eight knot (also called Listing's knot [1]) is the unique knot with a crossing number of four. This makes it the knot with the third-smallest possible crossing number, after the unknot and the trefoil knot. The figure-eight knot is a prime knot.
The first work of knot theory to include the Borromean rings was a catalog of knots and links compiled in 1876 by Peter Tait. [3] In recreational mathematics, the Borromean rings were popularized by Martin Gardner, who featured Seifert surfaces for the Borromean rings in his September 1961 "Mathematical Games" column in Scientific American. [19]