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• Unknot (category 0 bridge number knots and links)
  seen as a trivial knot In the mathematical theory of knots, the unknot, not knot, or trivial knot, is the least knotted of all knots. Intuitively, the
  5 KB (560 words) - 19:08, 6 February 2024
• Knot theory (category Knot theory) (section Adding knots)
  billion knots and links (Hoste 2005). The sequence of the number of prime knots of a given crossing number, up to crossing number 16, is 0, 0, 1, 1, 2
  48 KB (6,198 words) - 19:12, 6 February 2024
• Figure-eight knot (mathematics) (category 2 bridge number knots and links)
  Unique knot with a crossing number of four In knot theory, a figure-eight knot (also called Listing's knot) is the unique knot with a crossing number of four
  9 KB (986 words) - 18:54, 6 February 2024
• Knot invariant (category Knot invariants)
  diagram of the knot, and the bridge number, which is the minimum number of bridges for any diagram of the knot. Historically, many of the early knot invariants
  10 KB (1,266 words) - 00:08, 7 February 2024
• Link (knot theory) (section Tangles, string links, and braids)
  each strand required to lie at (0, 0), (0, 1), (1, 0), (1, 1), (2, 0), (2, 1), ... – i.e., connecting the integers, and ending in the same order that they
  8 KB (1,104 words) - 22:45, 6 February 2024
• Prime knot (category Knot invariants)
  non-trivial knot which cannot be written as the knot sum of two non-trivial knots. Knots that are not prime are said to be composite knots or composite
  3 KB (288 words) - 21:40, 6 February 2024
• Crossing number (knot theory) (category Knot invariants)
  to crossing number. Other numerical knot invariants include the bridge number, linking number, stick number, and unknotting number. "On Knots I, II, III′"
  5 KB (565 words) - 22:45, 6 February 2024
• Borromean rings (category 6 crossing number knots and links) (section Number theory)
  In the tables of knots and links in Dale Rolfsen's 1976 book Knots and Links, extending earlier listings in the 1920s by Alexander and Briggs, the Borromean
  42 KB (4,468 words) - 20:52, 8 February 2024
• Bridge number (category Knot invariants)
  of K1 and K2, then the bridge number of K is one less than the sum of the bridge numbers of K1 and K2. Crossing number Linking number Stick number Unknotting
  3 KB (366 words) - 22:55, 6 February 2024
• Alternating knot (category Knot invariants)
  diagram. Many of the knots with crossing number less than 10 are alternating. This fact and useful properties of alternating knots, such as the Tait conjectures
  6 KB (693 words) - 16:41, 6 February 2024
• (−2,3,7) pretzel knot (category 0 Arf invariant knots and links)
  Fintushel and Ronald J. Stern), is an important example of a pretzel knot which exhibits various interesting phenomena under three-dimensional and four-dimensional
  2 KB (138 words) - 20:13, 6 February 2024
• 2-bridge knot (category Knot theory)
  nontrivial knot. Other names for 2-bridge knots are rational knots, 4-plats, and Viergeflechte for 'four braids'. 2-bridge links are defined similarly as above
  3 KB (302 words) - 15:24, 6 February 2024
• Jones polynomial (category Knot theory) (section Link with quantum knot invariants)
   175. ISBN 978-0-387-98254-0. https://www.springer.com/mathematics/geometry/book/978-0-387-98254-0.  Thistlethwaite, Morwen (2001). "Links with trivial Jones
  17 KB (2,344 words) - 19:41, 6 February 2024
• Whitehead link (category 3 braid number knots and links)
  towards the linking number. Because the remaining crossings have equal numbers of under and over crossings on each loop, its linking number is 0. It is not isotopic
  6 KB (622 words) - 16:01, 6 February 2024
• Conway notation (knot theory) (category Knot theory)
  mi.sanu.ac.rs. "Conway Notation", The Knot Atlas. Conway, J.H. (1970). "An Enumeration of Knots and Links, and Some of Their Algebraic Properties". in
  3 KB (363 words) - 20:07, 6 February 2024
• Tait conjectures (category Knot theory) (section Crossing number of alternating knots)
  to all knots, or just to alternating knots. It turns out that most of them are only true for alternating knots. In the Tait conjectures, a knot diagram
  6 KB (672 words) - 14:48, 6 February 2024
• Stick number (category Knot invariants)
  stick number for any nontrivial knot. There are few knots whose stick number can be determined exactly. Gyo Taek Jin determined the stick number of a
  5 KB (546 words) - 18:55, 8 February 2024
• List of mathematical knots and links (category Knot theory) (section Knots)
  mathematical knots and links. See also list of knots, list of geometric topology topics. 01 knot/Unknot - a simple un-knotted closed loop 31 knot/Trefoil knot
  3 KB (419 words) - 17:53, 8 February 2024
• Carrick mat (category 3 bridge number knots and links)
  flat, it can be used as a woggle. List of knots Budworth, Geoffrey (1999). The Ultimate Encyclopedia of Knots & Ropework. London: Hermes House. p. 227. 
  3 KB (213 words) - 00:14, 7 February 2024
• L10a140 link (category 3 braid number knots and links)
  the second in an infinite series of Brunnian links beginning with the Borromean rings. So if the blue and yellow loops have only one twist along each side
  6 KB (831 words) - 17:40, 6 February 2024

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