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

From Wikipedia, the free encyclopedia

 A twist knot with six half-twists.
A twist knot with six half-twists.

In knot theory, a branch of mathematics, a twist knot is a knot obtained by repeatedly twisting a closed loop and then linking the ends together. (That is, a twist knot is any Whitehead double of an unknot.) The twist knots are an infinite family of knots, and are considered the simplest type of knots after the torus knots.

YouTube Encyclopedic

  • 1/3
    Views:
    1 856
    5 162
    5 876
  • Aaron Lauda: Math with a Twist
  • Knot Theory, Experimental Mathematics, and 3D Printing
  • How Mathematics gets into Knots - LMS 1987

Transcription

Contents

Construction

A twist knot is obtained by linking together the two ends of a twisted loop. Any number of half-twists may be introduced into the loop before linking, resulting in an infinite family of possibilities. The following figures show the first few twist knots:

Properties

 The four half-twist stevedore knot is created by passing the one end of an unknot with four half-twists through the other.
The four half-twist stevedore knot is created by passing the one end of an unknot with four half-twists through the other.

All twist knots have unknotting number one, since the knot can be untied by unlinking the two ends. Every twist knot is also a 2-bridge knot.[1] Of the twist knots, only the unknot and the stevedore knot are slice knots.[2] A twist knot with half-twists has crossing number . All twist knots are invertible, but the only amphichiral twist knots are the unknot and the figure-eight knot.

Invariants

The invariants of a twist knot depend on the number of half-twists. The Alexander polynomial of a twist knot is given by the formula

and the Conway polynomial is

When is odd, the Jones polynomial is

and when is even, it is

References

  1. ^ Rolfsen, Dale (2003). Knots and links. Providence, R.I: AMS Chelsea Pub. p. 114. ISBN 0-8218-3436-3. 
  2. ^ Weisstein, Eric W. "Twist Knot". MathWorld. 
This page was last edited on 31 October 2016, at 15:02.
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.