Prime knots and links | Knot invariants | Knots (knot theory)
In knot theory, a prime knot or prime link is a knot that is, in a certain sense, indecomposable. Specifically, it is a 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 links. It can be a nontrivial problem to determine whether a given knot is prime or not. A family of examples of prime knots are the torus knots. These are formed by wrapping a circle around a torus p times in one direction and q times in the other, where p and q are coprime integers. Knots are characterized by their crossing numbers. The simplest prime knot is the trefoil with three crossings. The trefoil is actually a (2, 3)-torus knot. The figure-eight knot, with four crossings, is the simplest non-torus knot. For any positive integer n, there are a finite number of prime knots with n crossings. The first few values (sequence in the OEIS) are given in the following table. Enantiomorphs are counted only once in this table and the following chart (i.e. a knot and its mirror image are considered equivalent). (Wikipedia).
This step by step guide demonstrates tying 15 types: 00:36 Overhand 01:22 Square 02:36 Figure Eight 03:40 Bowline, 05:29 Running 06:19 Half, 07:45 Timber, 09:42 Rolling, 10:43 Clove Hitches 11:30 Cat's Paw 12:58 Single, 14:40 Double Sheet or Becket Bends 15:30 Fisherman's, 17:09 Doubl
From playlist How To Tutorials
Minimal ropelength prime knots
Jason Cantarella's minimal ropelength prime knots: http://www.thingiverse.com/DesignByNumbers/designs/page:1?sort=&filter=&search=prime+knot Ball joint chain: http://shpws.me/EJzQ
From playlist 3D printing
Link: https://www.geogebra.org/m/a72HSgzU
From playlist Geometry: Challenge Problems
This knot is very useful for adjusting tie downs quickly and easily. For example, a tarp could be held down by a series of these knots and be made very tight so the wind cannot make it rise, and easily be removed simply by sliding the knots later. A taut line knot is also used to keep larg
From playlist Practical Projects & Skills
Link: https://www.geogebra.org/m/jUevutzZ
From playlist Geometry: Challenge Problems
Link: https://www.geogebra.org/m/bd69d6u4
From playlist Geometry: Challenge Problems
Link: https://www.geogebra.org/m/JEk3MHvc
From playlist Geometry: Challenge Problems
Do KNOT watch this video! #SoME1
This video is an entry to the 3Blue1Brown, The Summer of Math Exposition, about proving the existence of prime knots and the interesting steps towards the result. Some images produced with SeifertView, Jarke J. van Wijk, Technische Universiteit Eindhoven. Download SeifertView at the link
From playlist Summer of Math Exposition Youtube Videos
Is the Conway knot slice? (After Lisa Piccirillo)
This is a talk on the recent work by Lisa Piccirillo showing that the Conway know is not a slice knot. We first review the definitions of the Conway know and slice knots, and then give an overview of her proof. The paper on this by Lisa Piccirillo can be found at https://arxiv.org/pdf/1
From playlist Math talks
Primes and Knots - Akshay Venkatesh
Public Lecture: Primes and Knots - October 25, 2019 Akshay Venkatesh, Robert and Luisa Fernholz Professor School of Mathematics, IAS In mathematics, there are many surprising parallels between problems in the theory of numbers and questions in three-dimensional geometry. Akshay Venkatesh
From playlist Mathematics
Hyperbolic Knot Theory (Lecture - 2) by Abhijit Champanerkar
PROGRAM KNOTS THROUGH WEB (ONLINE) ORGANIZERS: Rama Mishra, Madeti Prabhakar, and Mahender Singh DATE & TIME: 24 August 2020 to 28 August 2020 VENUE: Online Due to the ongoing COVID-19 pandemic, the original program has been canceled. However, the meeting will be conducted through onl
From playlist Knots Through Web (Online)
Knotty Problems - Marc Lackenby
Knots are a familiar part of everyday life, for example tying your tie or doing up your shoe laces. They play a role in numerous physical and biological phenomena, such as the untangling of DNA when it replicates. However, knot theory is also a well-developed branch of pure mathematics.
From playlist Oxford Mathematics Public Lectures
Link: https://www.geogebra.org/m/ZY87MGd5
From playlist Geometry: Challenge Problems
Jessica Purcell - Lecture 1 - Hyperbolic knots and alternating knots
Jessica Purcell, Monash University Title: Hyperbolic knots and alternating knots Hyperbolic geometry has been used since around the mid-1970s to study knot theory, but it can be difficult to relate geometry of knots to a diagram of a knot. However, many results from the 1980s and beyond s
From playlist 39th Annual Geometric Topology Workshop (Online), June 6-8, 2022
They are knot what you think! More links & stuff in full description below ↓↓↓ Primes, Composites and the usefulness of knots.... Second in a series of videos about knots. Here we again speak with Carlo H. Séquin from UC Berkeley. More videos to come at: http://bit.ly/Knot-a-Phile Edit an
From playlist Carlo Séquin on Numberphile
Link: https://www.geogebra.org/m/bCFvje77
From playlist Geometry: Challenge Problems
Satellite operations and Legendrian knot theory - John Etnyre
Satellite operations and Legendrian knot theory Augmentations and Legendrians at the IAS Topic: Satellite operations and Legendrian knot theory Speaker: John Etnyre Date: Thursday, February 11 Satellite operations are a common way to create interesting knot types in the smooth category. I
From playlist Mathematics
Overview of Knots and Motivation of Quandels by Mohamed Elhamdadi
PROGRAM KNOTS THROUGH WEB (ONLINE) ORGANIZERS: Rama Mishra, Madeti Prabhakar, and Mahender Singh DATE & TIME: 24 August 2020 to 28 August 2020 VENUE: Online Due to the ongoing COVID-19 pandemic, the original program has been canceled. However, the meeting will be conducted through onl
From playlist Knots Through Web (Online)
Link: https://www.geogebra.org/m/cjS3b6Zr
From playlist Geometry: Challenge Problems