Knot theory

From WikiMD's Food, Medicine & Wellness Encyclopedia

Tabela_de_nós_matemáticos_01,_crop
TrefoilKnot_01
KellsFol034rXRhoDet3
Peter_Guthrie_Tait._Mezzotint_by_J._Faed_after_Sir_G._Reid._Wellcome_V0006622
Tenfold_Knottiness,_plate_IX
Reidemeister_move_1

File:Frame left_|thumb|Frame_left]]_]] Knot theory is a branch of topology that studies mathematical knots. While inspired by knots which appear in daily life in shoelaces and rope, a mathematical knot differs in that the ends are joined together so that it cannot be undone. In mathematical terms, a knot is an embedding of a circle in 3-dimensional Euclidean space, \(\mathbb{R}^3\). Two knots are considered equivalent if one can be transformed into the other via a continuous deformation, known as an isotopy.

History[edit | edit source]

The origins of knot theory can be traced back to the 19th century when Lord Kelvin proposed that atoms were knots in the aether. This idea led to the first systematic tabulation of knots by Peter Guthrie Tait, Charles Niven, and Thomas Kirkman. Although Kelvin's theory was eventually discarded, the mathematical study of knots continued to develop.

Basic Concepts[edit | edit source]

Knot Invariants[edit | edit source]

A key aspect of knot theory is the study of knot invariants, which are properties of knots that remain unchanged under isotopy. Examples of knot invariants include the knot group, the Alexander polynomial, and the Jones polynomial.

Types of Knots[edit | edit source]

Knots can be classified into various types based on their properties. Some common types include:

Knot Diagrams[edit | edit source]

A knot diagram is a projection of a knot onto a plane, with information about the over and under crossings. Knot diagrams are useful for visualizing and manipulating knots.

Applications[edit | edit source]

Knot theory has applications in various fields including biology, where it is used to study the structure of DNA and other molecules, and in chemistry, where it helps in understanding the properties of certain chemical compounds. It also has applications in physics, particularly in the study of quantum field theory and statistical mechanics.

Related Pages[edit | edit source]

References[edit | edit source]

External Links[edit | edit source]

Wiki.png

Navigation: Wellness - Encyclopedia - Health topics - Disease Index‏‎ - Drugs - World Directory - Gray's Anatomy - Keto diet - Recipes

Search WikiMD


Ad.Tired of being Overweight? Try W8MD's physician weight loss program.
Semaglutide (Ozempic / Wegovy and Tirzepatide (Mounjaro / Zepbound) available.
Advertise on WikiMD

WikiMD is not a substitute for professional medical advice. See full disclaimer.

Credits:Most images are courtesy of Wikimedia commons, and templates Wikipedia, licensed under CC BY SA or similar.

Contributors: Prab R. Tumpati, MD