In mathematics, a knot is an embedding of the circle S1 into three-dimensional Euclidean space, R3 (also known as E3). Often two knots are considered equivalent if they are ambient isotopic, that is, if there exists a continuous deformation of R3 which takes one knot to the other. A crucial difference between the standard mathematical and conventional notions of a knot is that mathematical knots are closed — there are no ends to tie or untie on a mathematical knot. Physical properties such as friction and thickness also do not apply, although there are mathematical definitions of a knot that take such properties into account. The term knot is also applied to embeddings of S j in Sn, especially in the case j = n − 2. The branch of mathematics that studies knots is known as knot theory and has many relations to graph theory. (Wikipedia).
Algebraic topology: Fundamental group of a knot
This lecture is part of an online course on algebraic topology. We calculate the fundamental group of (the complement of) a knot, and give a couple of examples. For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj52yxQGxQoxwOtjIEtxE2BWx
From playlist Algebraic topology
Untangling the beautiful math of KNOTS
Visit ► https://brilliant.org/TreforBazett/ to help you learn STEM topics for free, and the first 200 people will get 20% off an annual premium subscription. Check out my MATH MERCH line in collaboration with Beautiful Equations ►https://www.beautifulequation.com/pages/trefor Suppose yo
From playlist Cool Math Series
Link: https://www.geogebra.org/m/a72HSgzU
From playlist Geometry: Challenge Problems
Link: https://www.geogebra.org/m/JEk3MHvc
From playlist Geometry: Challenge Problems
What's a knot? Geometry Terms and Definitions
A mathematical definition of a knot. Geometer: Louise McCartney Artwork: Kelly Vivanco Director: Michael Harrison Written & Produced by Kimberly Hatch Harrison and Michael Harrison ♦♦♦♦♦♦♦♦♦♦ Ways to support our channel: ► Join our Patreon : https://www.patreon.com/socratica ► Mak
From playlist Socratica: The Geometry Glossary Series
Three Knot-Theoretic Perspectives on Algebra - Zsuzsanna Dancso
Zsuzsanna Dancso University of Toronto; Institute for Advanced Study September 21, 2011 For more videos, visit http://video.ias.edu
From playlist Mathematics
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
Link: https://www.geogebra.org/m/cjS3b6Zr
From playlist Geometry: Challenge Problems
How Knots Help Us Understand the World
Knots are everywhere in our daily lives, but a new branch of mathematics is taking things to the next level. Hosted by: Hank Green SciShow has a spinoff podcast! It's called SciShow Tangents. Check it out at http://www.scishowtangents.org ---------- Support SciShow by becoming a patron o
From playlist Uploads
Mathematics as Metaphor - Curtis McMullen (Harvard University)
Public lecture
From playlist Mathematics Research Center
Jessica Purcell: Triangulations, geometry and knots
In this research profile, upcoming SMRI visitor Jessica Purcell describes the open questions in the study of 3-manifolds and how her fascination with mathematical knots began. Jessica Purcell is a Professor in the School of Mathematical Sciences and Associate Dean of Research (Faculty of
From playlist SMRI Interviews
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
Knots and Quantum Theory - Edward Witten
Edward Witten Institute for Advanced Study December 15, 2010 A knot is simply a tangled loop in ordinary three-dimensional space, such as often causes us frustration in everyday life. Knots are also the subject of a rather rich mathematical theory. In the last three decades, it has unexpec
From playlist Natural Sciences
First in a series of videos about knots. Here we have Carlo H. Séquin from UC Berkeley. More links & stuff in full description below ↓↓↓ More videos to come at: http://bit.ly/Knot-a-Phile Edit and animation by Pete McPartlan. Film and interview by Brady Haran With thanks to Rob Scharein
From playlist Carlo Séquin on Numberphile
Sir Michael Atiyah - The Mysteries of Space [1991]
The 64th annual Gibbs Lecture was given by Sir Michael Atiyah, Fellow of the Royal Society, of Trinity College, Cambridge, England. At a conference in San Francisco, California in January 1991, he delivered "Physics and the mysteries of space", which was filmed and made available on videot
From playlist Mathematics
Knots and Quantum Theory | Edward Witten, Charles Simonyi Professor
Edward Witten, Charles Simonyi Professor, School of Natural Sciences, Institute for Advanced Study http://www.ias.edu/people/faculty-and-emeriti/witten A knot is more or less what you think it is—a tangled mess of string in ordinary three-dimensional space. In the twentieth century, mathe
From playlist Natural Sciences
Link: https://www.geogebra.org/m/bd69d6u4
From playlist Geometry: Challenge Problems
2020's Biggest Breakthroughs in Math and Computer Science
For mathematicians and computer scientists, 2020 was full of discipline-spanning discoveries and celebrations of creativity. We'd like to take a moment to recognize some of these achievements. 1. A landmark proof simply titled “MIP* = RE" establishes that quantum computers calculating wit
From playlist Discoveries