Knots

• Unknot
  Unknot
  The unknot arises in the mathematical theory of knots. Intuitively, the unknot is a closed loop of rope without a knot in it. A knot theorist would describe the unknot as an image of any embedding that can be deformed, i.e. ambient-isotoped, to the standard unknot, i.e. the embedding of the...
  
  
• Trefoil knot
  Trefoil knot
  In topology, a branch of mathematics, the trefoil knot is the simplest example of a nontrivial knot. The trefoil can be obtained by joining together the two loose ends of a common overhand knot, resulting in a knotted loop...
  
  
• Figure-eight knot (mathematics)
  Figure-eight knot (mathematics)
  In knot theory, a figure-eight knot is the unique knot with a crossing number of four. This is the smallest possible crossing number except for the unknot and trefoil knot...
  
  
• Cinquefoil knot
  Cinquefoil knot
  In knot theory, the cinquefoil knot, also known as Solomon's seal knot or the pentafoil knot, is one of two knots with crossing number five, the other being the three-twist knot. It is listed as the 51 knot in the Alexander-Briggs notation, and can also be described as the -torus knot...
  
  
• Three-twist knot
  Three-twist knot
  In knot theory, the three-twist knot is the twist knot with three-half twists. It is listed as the 52 knot in the Alexander-Briggs notation, and is one of two knots with crossing number five, the other being the cinquefoil knot....
  
  
• Stevedore knot (mathematics)
  Stevedore knot (mathematics)
  In knot theory, the stevedore knot is one of three prime knots with crossing number six, the others being the 62 knot and the 63 knot. The stevedore knot is listed as the 61 knot in the Alexander–Briggs notation, and it can also be described as a twist knot with four twists, or as the pretzel...
  
  
• 6₂ knot
  6₂ knot
  In knot theory, the 62 knot is one of three prime knots with crossing number six, the others being the stevedore knot and the 63 knot. This knot is sometimes referred to as the Miller Institute knot, because is appears in the logo of the Miller Institute for Basic Research in Science at the...
  
  
• 6₃ knot
  6₃ knot
  In knot theory, the 63 knot is one of three prime knots with crossing number six, the others being the stevedore knot and the 62 knot.Like the figure-eight knot, the 63 knot is amphichiral, meaning that it is indistinguishable from its own mirror image...
  
  
• 7₁ knot
  7₁ knot
  In knot theory, the 71 knot, also known as the septoil knot, the septafoil knot, or the -torus knot, is one of seven prime knots with crossing number seven. It is the simplest torus knot after the trefoil and cinquefoil....
  
  
• Square knot (mathematics)
  Square knot (mathematics)
  In knot theory, the square knot is a composite knot obtained by taking the connected sum of two trefoil knots. It is closely related to the granny knot, which is also a connected sum of two trefoils...
  
  
• Granny knot (mathematics)
  Granny knot (mathematics)
  In knot theory, the granny knot is a composite knot obtained by taking the connected sum of two identical trefoil knots. It is closely related to the square knot, which can also be described as a connected sum of two trefoils...
  
  
• pretzel knot
• (p, q)-torus knot
  Torus knot
  In knot theory, a torus knot is a special kind of knot that lies on the surface of an unknotted torus in R3. Similarly, a torus link is a link which lies on the surface of a torus in the same way. Each torus knot is specified by a pair of coprime integers p and q. A torus link arises if p and q...
  
  

Links

• Borromean rings
  Borromean rings
  In mathematics, the Borromean rings consist of three topological circles which are linked and form a Brunnian link, i.e., removing any ring results in two unlinked rings.- Mathematical properties :...
  
  
• Brunnian link
  Brunnian link
  In knot theory, a branch of mathematics, a Brunnian link is a nontrivial link that becomes trivial if any component is removed. In other words, cutting any loop frees all the other loops ....
  
  
• Hopf link
  Hopf link
  thumb|right|[[Skein relation]] for the Hopf link.In mathematical knot theory, the Hopf link, named after Heinz Hopf, is the simplest nontrivial link with more than one component. It consists of two circles linked together exactly once...
  
  
• Pretzel link
  Pretzel link
  In knot theory, a branch of mathematics, a pretzel link is a special kind of link. A pretzel link which is also a knot is a pretzel knot....
  
  
• Solomon's knot
  Solomon's knot
  Solomon's knot is the most common name for a traditional decorative motif used since ancient times, and found in many cultures...
  
   (a "link" rather than a "knot" according to the conventions of the mathematical theory of knots)
• Unlink
  Unlink
  In the mathematical field of knot theory, the unlink is a link that is equivalent to finitely many disjoint circles in the plane.- Properties :...
  
  
• Whitehead link
  Whitehead link
  In knot theory, the Whitehead link, discovered by J.H.C. Whitehead, is one of the most basic links.J.H.C. Whitehead spent much of the 1930s looking for a proof of the Poincaré conjecture...
  
  

External links