Reference Article

from Wikipedia, the free encyclopedia

Knot theory

Knot theory is the mathematical branch of topology that studies mathematical knots, which are defined as embeddings of a circle in 3-dimensional Euclidean space, R3.

This is basically equivalent to a conventional knotted string with the ends joined together to prevent it from becoming undone.

Two mathematical knots are equivalent if one can be transformed into the other via a deformation of R3 upon itself (known as an ambient isotopy); these transformations correspond to manipulations of a knotted string that do not involve cutting the string or passing the string through itself.

Knots can be described in various ways.

Given a method of description, however, there may be more than one description that represents the same knot.

For example, a common method of describing a knot is a planar diagram.

But any given knot can be drawn in many different ways using a planar diagram.

Therefore, a fundamental problem in knot theory is determining when two descriptions represent the same knot.

One way of distinguishing knots is by using a knot invariant, a "quantity" which remains the same even with different descriptions of a knot.

The concept of a knot has been extended to higher dimensions by considering n-dimensional spheres in m-dimensional Euclidean space.

This was investigated most actively in the period 1960-1980, when a number of breakthroughs were made.

In recent years, low dimensional phenomena have garnered the most interest.

Research in knot theory began with the creation of knot tables and the systematic tabulation of knots.

While tabulation remains an important task, today's researchers have a wide variety of backgrounds and goals.

In the last 30 years, knot theory has also become a tool in applied mathematics.

Chemists and biologists use knot theory to understand, for example, chirality of molecules and the actions of enzymes on DNA.

Note: This article excerpts material from the Wikipedia article "Knot theory", which is released under the GNU Free Documentation License.

See the following related content on ScienceDaily:


Related Videos

last updated on 2014-09-30 at 6:27 pm EDT

How to Plan a Wedding Menu

How to Plan a Wedding Menu

Howdini (Dec. 15, 2011) — Planning a wedding? Then you're no doubt planning a menu, too. And you probably have more options than you think. Here's the latest in wedding menu trends from Carley Roney of The Knot.
Powered by NewsLook.com
Nobel in Physics Goes to Englert and Higgs

Nobel in Physics Goes to Englert and Higgs

AP (Oct. 8, 2013) — Describing how subatomic particles get mass wins Nobel physics prize for Francois Englert of Belgium and Peter Higgs of Britain for theory on how the most basic building blocks of the universe acquire mass. (Oct. 8)
Powered by NewsLook.com
Stephen Hawking: Quality of Life Is Pretty Good

Stephen Hawking: Quality of Life Is Pretty Good

AP (June 18, 2012) — As part of the 2012 Seattle Science Festival, renowned physicist Stephen Hawking took the stage Saturday night to discuss time travel, the search for a scientific 'theory of everything,' and his hopes to some day win a Nobel prize.
Powered by NewsLook.com
Scientists Testing If Universe Is Just Computer Simulation

Scientists Testing If Universe Is Just Computer Simulation

Buzz60 (Dec. 14, 2012) — German scientists are testing a theory that 'The Matrix' is real and the universe is really just a computer simulation. The scientists cite the laws of physics and constraints on energy particles as evidence. And, they believe we're not the first civilization advanced enough to run these complex universe models. But not everyone in the science community is thrilled with this assertion.
Powered by NewsLook.com

Related Stories


Share This



Search ScienceDaily

Number of stories in archives: 140,361

Find with keyword(s):
 
Enter a keyword or phrase to search ScienceDaily for related topics and research stories.

Save/Print:
Share:  

Breaking News:
from the past week

In Other News

... from NewsDaily.com

Science News

Health News

Environment News

Technology News



Save/Print:
Share:  

Free Subscriptions


Get the latest science news with ScienceDaily's free email newsletters, updated daily and weekly. Or view hourly updated newsfeeds in your RSS reader:

Get Social & Mobile


Keep up to date with the latest news from ScienceDaily via social networks and mobile apps:

Have Feedback?


Tell us what you think of ScienceDaily -- we welcome both positive and negative comments. Have any problems using the site? Questions?
Mobile iPhone Android Web
Follow Facebook Twitter Google+
Subscribe RSS Feeds Email Newsletters
Latest Headlines Health & Medicine Mind & Brain Space & Time Matter & Energy Computers & Math Plants & Animals Earth & Climate Fossils & Ruins