To install click the Add extension button. That's it.

The source code for the WIKI 2 extension is being checked by specialists of the Mozilla Foundation, Google, and Apple. You could also do it yourself at any point in time.

4,5
Kelly Slayton
Congratulations on this excellent venture… what a great idea!
Alexander Grigorievskiy
I use WIKI 2 every day and almost forgot how the original Wikipedia looks like.
Live Statistics
English Articles
Improved in 24 Hours
Added in 24 Hours
Languages
Recent
Show all languages
What we do. Every page goes through several hundred of perfecting techniques; in live mode. Quite the same Wikipedia. Just better.
.
Leo
Newton
Brights
Milds

Unknotting number

From Wikipedia, the free encyclopedia

 Trefoil knot without 3-fold symmetry being unknotted by one crossing switch.
Trefoil knot without 3-fold symmetry being unknotted by one crossing switch.

In the mathematical area of knot theory, the unknotting number of a knot is the minimum number of times the knot must be passed through itself (crossing switch) to untie it. If a knot has unknotting number , then there exists a diagram of the knot which can be changed to unknot by switching crossings.[1] The unknotting number of a knot is always less than half of its crossing number.[2]

Any composite knot has unknotting number at least two, and therefore every knot with unknotting number one is a prime knot. The following table show the unknotting numbers for the first few knots:

In general, it is relatively difficult to determine the unknotting number of a given knot. Known cases include:

  • The unknotting number of a nontrivial twist knot is always equal to one.
  • The unknotting number of a -torus knot is equal to .
  • The unknotting numbers of prime knots with nine or fewer crossings have all been determined.[3] (The unknotting number of the 1011 prime knot is unknown.)

YouTube Encyclopedic

  • 1/3
    Views:
    925 644
    636
    2 601 234
  • Perfect Shapes in Higher Dimensions - Numberphile
  • Knot Floer homology - Prof. Peter Ozsváth
  • 4th Dimension explained

Transcription

Contents

Other numerical knot invariants

See also

References

  1. ^ Adams, Colin Conrad (2004). The knot book: an elementary introduction to the mathematical theory of knots. Providence, Rhode Island: American Mathematical Society. p. 56. ISBN 0-8218-3678-1. 
  2. ^ Taniyama, Kouki (2009), "Unknotting numbers of diagrams of a given nontrivial knot are unbounded", Journal of Knot Theory and its Ramifications, 18 (8): 1049–1063, doi:10.1142/S0218216509007361, MR 2554334 .
  3. ^ Weisstein, Eric W. "Unknotting Number". MathWorld. 

External links

This page was last modified on 15 April 2014, at 06:12.
Basis of this page is in Wikipedia. Text is available under the CC BY-SA 3.0 Unported License. Non-text media are available under their specified licenses. Wikipedia® is a registered trademark of the Wikimedia Foundation, Inc. WIKI 2 is an independent company and has no affiliation with Wikimedia Foundation.