The Knot Atlas

Last updated

The Knot Atlas is a website, an encyclopedia rather than atlas, dedicated to knot theory. It and its predecessor were created by mathematician Dror Bar-Natan, who maintains the current site with Scott Morrison. According to Schiller, the site contains, "beautiful illustrations and detailed information about knots," as does KnotPlot.com. [1] According to the site itself, it is a knot atlas (collection of maps), theory database, knowledge base, and "a home for some computer programs". [2]

Related Research Articles

Figure-eight knot (mathematics) unique knot with a crossing number of four

In knot theory, a figure-eight knot is the unique knot with a crossing number of four. This makes it the knot with the third-smallest possible crossing number, after the unknot and the trefoil knot. The figure-eight knot is a prime knot.

Friedrich Schiller German poet, philosopher, historian, and playwright

Johann Christoph Friedrich von Schiller was a German poet, philosopher, physician, historian and playwright. During the last seventeen years of his life (1788–1805), Schiller developed a productive, if complicated, friendship with the already famous and influential Johann Wolfgang von Goethe. They frequently discussed issues concerning aesthetics, and Schiller encouraged Goethe to finish works he left as sketches. This relationship and these discussions led to a period now referred to as Weimar Classicism. They also worked together on Xenien, a collection of short satirical poems in which both Schiller and Goethe challenge opponents of their philosophical vision.

Knot invariant function of a knot that takes the same value for equivalent knots

In the mathematical field of knot theory, a knot invariant is a quantity defined for each knot which is the same for equivalent knots. The equivalence is often given by ambient isotopy but can be given by homeomorphism. Some invariants are indeed numbers, but invariants can range from the simple, such as a yes/no answer, to those as complex as a homology theory. Research on invariants is not only motivated by the basic problem of distinguishing one knot from another but also to understand fundamental properties of knots and their relations to other branches of mathematics.

John C. Baez American mathematician

John Carlos Baez is an American mathematical physicist and a professor of mathematics at the University of California, Riverside (UCR) in Riverside, California. He is known for his work on spin foams in loop quantum gravity. For some time, his research had focused on applications of higher categories to physics and other things.

Red knot Species of bird

The red knot is a medium-sized shorebird which breeds in tundra and the Arctic Cordillera in the far north of Canada, Europe, and Russia. It is a large member of the Calidris sandpipers, second only to the great knot. Six subspecies are recognised.

Nova is an American popular science television program produced by WGBH Boston since 1974. It is broadcast on PBS in the U.S., and in more than 100 other countries. The program has won many major television awards.

Knot (mathematics) embedding of a circle in R³

In mathematics, a knot is an embedding of a circle S1 in 3-dimensional Euclidean space, R3, considered up to continuous deformations (isotopies). 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 Sj in Sn, especially in the case j = n − 2. The branch of mathematics that studies knots is known as knot theory, and has many simple relations to graph theory.

William Tell folk hero of Switzerland

William Tell is a folk hero of Switzerland. According to the legend, Tell was an expert marksman with the crossbow who assassinated Albrecht Gessler, a tyrannical reeve of the Austrian dukes of the House of Habsburg positioned in Altdorf, in the canton of Uri. Tell's defiance and tyrannicide encouraged the population to open rebellion and a pact against the foreign rulers with neighbouring Schwyz and Unterwalden, marking the foundation of the Swiss Confederacy.

The Schiller Institute is a German based political and economic think tank founded by Helga Zepp-LaRouche, with stated members in 50 countries. It is among the principal organizations of the LaRouche movement. The institute's stated aim is to apply the ideas of the poet and philosopher Friedrich Schiller to what it calls the "contemporary world crisis." Their constitution, adopted in 1984, rails against international financial institutions and other supranational bodies, without naming any, for causing a state of tyranny in the world, especially amongst developing nations.

Morrison Formation Rock formation

The Morrison Formation is a distinctive sequence of Upper Jurassic sedimentary rock found in the western United States which has been the most fertile source of dinosaur fossils in North America. It is composed of mudstone, sandstone, siltstone, and limestone and is light gray, greenish gray, or red. Most of the fossils occur in the green siltstone beds and lower sandstones, relics of the rivers and floodplains of the Jurassic period.

F. C. S. Schiller German-born British pragmatist philosopher

Ferdinand Canning Scott Schiller, usually cited as F. C. S. Schiller, was a German-British philosopher. Born in Altona, Holstein, Schiller studied at the University of Oxford, later was a professor there, after being invited back after a brief time at Cornell University. Later in his life he taught at the University of Southern California. In his lifetime he was well known as a philosopher; after his death his work was largely forgotten.

A slice knot is a type of mathematical knot.

In the mathematical field of knot theory, a chiral knot is a knot that is not equivalent to its mirror image. An oriented knot that is equivalent to its mirror image is an amphichiral knot, also called an achiral knot or amphicheiral knot. The chirality of a knot is a knot invariant. A knot's chirality can be further classified depending on whether or not it is invertible.

Scott Morrison 30th Prime Minister of Australia

Scott John Morrison is an Australian politician who has been Prime Minister of Australia and leader of the Liberal Party since August 2018. He previously served in Cabinet from 2013 to 2018, including as Treasurer.

Dinosaur Ridge ridge in Colorado, United States

Dinosaur Ridge is a segment of the Dakota Hogback in the Morrison Fossil Area National Natural Landmark located in Jefferson County, Colorado, near the town of Morrison and just west of Denver.

Solomons knot Motif with two doubly-interlinked loops

Solomon's knot is a traditional decorative motif used since ancient times, and found in many cultures. Despite the name, it is classified as a link, and is not a true knot according to the definitions of mathematical knot theory.

David Morrison (astrophysicist) American astronomer


David Morrison is an American astronomer, a senior scientist at the Solar System Exploration Research Virtual Institute, at NASA Ames Research Center in Mountain View, California. Morrison is the former director of the Carl Sagan Center for Study of Life in the Universe at the SETI Institute and of the NASA Lunar Science Institute. He is the past Director of Space at NASA Ames. Morrison is credited as a founder of the multi-disciplinary field of astrobiology. Morrison is best known for his work in risk assessment of near Earth objects such as asteroids and comets. Asteroid 2410 Morrison was named in his honor. Morrison is also known for his "Ask an Astrobiologist" series on NASA's website where he provides answers to questions submitted by the public. He has published 12 books and over 150 papers primarily on planetary science, astrobiology and near earth objects.

LoDaisKa Site United States historic place

The LoDaisKa Site is a prominent archaeological site in the U.S. state of Colorado, located within a rockshelter near Morrison. The rockshelter was first inhabited by people of the Archaic through the Middle Ceramic period, generally spanning 3000 BC to 1000 AD.

Sierra Prieta

The Sierra Prieta is a 14-mi (23 km), long mountain range in central-northwest Arizona. The range is the mountainous region west of Prescott, with prominent Thumb Butte, 6,514 feet (1,985 m), a volcanic plug, on the city's west perimeter.

References

  1. Schiller, Christoph (2012). Motion Mountain, The Adventure of Physics – Vol. 5: Motion Inside Matter – Pleasure, Technology and Stars, p. 272. MotionMountain.net.
  2. " Knot Atlas:About ", The Knot Atlas .