Knot theory is the branch of topology that studies mathematical knots, embeddings of a circle in three-dimensional space whose ends are joined so they cannot be undone. It emerged from nineteenth century physical speculation that atoms were knotted vortices in the ether, which motivated the first systematic knot tables in the 1880s, and it survived the collapse of that physical theory to become a mathematical field in its own right. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/
Facts
Central QuestionGiven two different-looking descriptions of a closed loop embedded in three-dimensional space, is there a way, ideally a computable one, to tell whether they represent the same knot? 1 Key DebateWhether knot theory's founding motivation, Lord Kelvin's nineteenth century theory that atoms were stable knotted vortices in the ether, deserves credit as a genuine scientific origin given that the physical theory itself was entirely wrong; the systematic knot tables Peter Guthrie Tait built to catalogue possible vortex atoms in the 1880s outlived the physics that inspired them and became the field's own foundation. 1 Classification
Pure or Applied Connections
Associated With
Source Peter Guthrie Tait, Biography (MacTutor History of Mathematics)
Includes
Source Cinquefoil Knot (Wikipedia)
Source Conway knot (Wikipedia)
Source Wikipedia: Figure-eight knot (mathematics)
Source Hopf Link (Wikipedia)
Source Reidemeister move (Wikipedia)
Source Wikipedia: Trefoil knot
Source Volume Conjecture (Wikipedia)
Source Whitehead link (Wikipedia)
Source Writhe (Wikipedia)
Sources
1. Knot Theory (Wikipedia)
WikipediaDefinition and history sections
a knot is an embedding of a circle in 3-dimensional Euclidean space
Central questions, the recognition problem
two descriptions represent the same knot
Historical origins section
Lord Kelvin's theory that atoms were knots in the aether
View the Source Wikipedia: Trefoil knot
Includes: Trefoil Knot, Lead sentenceQuote, Includes: Trefoil Knot, Lead sentence
In knot theory, a branch of mathematics, the trefoil knot is the simplest example of a nontrivial knot.
Wikipedia: Figure-eight knot (mathematics)
Includes: Figure-Eight Knot, Lead sentenceQuote, Includes: Figure-Eight Knot, Lead sentence
In knot theory, a figure-eight knot (also called Listing's knot) is the unique knot with a crossing number of four.
Whitehead link (Wikipedia)
Includes: Whitehead Link, Lead sentenceQuote, Includes: Whitehead Link, Lead sentence
In knot theory, the Whitehead link, named for J.
Writhe (Wikipedia)
Hopf Link (Wikipedia)
Includes: Hopf Link, Lead sentenceQuote, Includes: Hopf Link, Lead sentence
In mathematical knot theory, the Hopf link is the simplest nontrivial link with more than one component.
Cinquefoil Knot (Wikipedia)
Includes: Cinquefoil Knot, Lead sentenceQuote, Includes: Cinquefoil Knot, Lead sentence
In knot theory, the cinquefoil knot, also known as Solomon's seal knot or the pentafoil knot, is one of two knots with crossing nu
Conway knot (Wikipedia)
Includes: Conway knot, Lead sentenceQuote, Includes: Conway knot, Lead sentence
In mathematics, specifically in knot theory, the Conway knot (or Conway's knot) is a particular knot with 11 crossings, named afte
Volume Conjecture (Wikipedia)
Reidemeister move (Wikipedia)
Includes: Reidemeister's Theorem, Lead sentenceQuote, Includes: Reidemeister's Theorem, Lead sentence
In the mathematical area of knot theory, a Reidemeister move is any of three local moves on a link diagram.
Reader Challenges (0)
No disputes yet. Spotted an error or a better source? Open the first one.
Sign in to dispute this or suggest a correction.