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...y and [[3-manifold]] theory, often the adjective "tame" is omitted. Smooth knots, for example, are always tame. Knots that are not tame are called '''wild''' and can have [[pathological (mathematics)|pathological]] behavior. ...

{{short description|Family of mathematical knots}} ...family of knots, and are considered the simplest type of knots after the [[torus knot]]s. ...

...le=The knot book: an elementary introduction to the mathematical theory of knots |publisher=American Mathematical Society |location=Providence, Rhode Island | journal = Journal of Knot Theory and its Ramifications ...

...projection onto the plane perpendicular to ''v'' gives a [[knot diagram]], and we can compute the crossing number, denoted ''n''(''v''). The average cross ...where projection doesn't give a knot diagram is a set of [[measure zero]] and ''n''(''v'') is [[locally constant]] when defined. ...

{{Short description|Conjecture in knot theory relating quantum invariants and hyperbolic geometry}} * [[torus knot]]s ...

...sted as the '''6₁ knot''' in the [[Alexander–Briggs notation]], and it can also be described as a [[twist knot]] with four half twists, or as t and its [[Jones polynomial]] is ...

...ually depicted in a highly-symmetric form, and so appears in the symbolism and/or artistic ornamentation of various cultures. ...hexagram can appear in non-interlaced versions, in which case they are not knots at all.) ...

...six, the others being the [[Stevedore knot (mathematics)|stevedore knot]] and the [[63 knot|6₃ knot]]. This knot is sometimes referred to as and its [[Jones polynomial]] is ...

...]. It is [[alternating knot|alternating]], [[hyperbolic knot|hyperbolic]], and [[amphichiral knot|fully amphichiral]]. and the [[Kauffman polynomial]] is ...

...e 52 knot.}}</ref> in the [[Alexander-Briggs notation]], and is one of two knots with [[crossing number (knot theory)|crossing number]] five, the other bein The three-twist knot is a [[prime knot]], and it is [[invertible knot|invertible]] but not [[amphichiral knot|amphichiral ...

...de. After her mother dies as well, Charlotte is brought to her grandmother and later wants to find the correct [[Shape of the universe|topology of the uni ...oposed a [[cosmological model]] where the [[shape of the universe]] is a 3-torus.<ref name="NYT">Overbeye, Dennis. ''New York Times'' 11 March 2003: Web. 1 ...

...ara1991}} This is a useful property because it prevents self-intersection and ensures the result under [[gradient descent]] is of the same [[knot type]]. ...s transformation]]s was demonstrated by [[Michael Freedman]], Zheng-Xu He, and [[Zhenghan Wang]] (1994) who used it to show the existence of a <math>C^{1, ...

...alizing in representation theory, symplectic geometry, algebraic geometry, and combinatorial algebra.<ref name="CV">{{cite web|title=Curriculum Vitae, Iva ==Education and career== ...

...als and Concepts: Some key concepts in Gordon Pask's Interaction of Actors and Conversation Theories. ''Constructivist Foundations''. 4(3): 151-158 (pp. 1 ...and Nature: A Necessary Unity" 1980). Pask's nexus of analogy, dependence and mechanical spin produces the differences that are central to [[cybernetics] ...

...m, but at the other side. If continued, the line meets the starting point, and is double the length of the original strip. This single continuous curve de ...of the edge of the original strip, and it comprises one-third of the width and twice the length of the original strip. ...

|death_date = {{death date and age|2008|11|24|1935|7|22}} ...han six]]; [[Stallings theorem about ends of groups]]; [[Stallings graphs and automata]] ...

| birth_date = {{Birth date and age|1958|4|8|df=y}} ...st=Deninger|first=Christopher|chapter=Some analogies between number theory and dynamical systems on foliated spaces|title=Doc. Math. (Bielefeld) Extra Vol ...

The following list is composed of objects, concepts, phenomena and processes that were discovered or invented by people from the [[Netherlands ...w ''Homo erectus'') found in Java in 1891. Estimated to be between 700,000 and 1,000,000 years old, at the time of their discovery the fossils of "[[Java ...

Egyptian inventions and discoveries are objects, processes or techniques which owe their existence === Government and Economy === ...