Translation and analysis of words by ChatGPT artificial intelligence
On this page you can get a detailed analysis of a word or phrase, produced by the best artificial intelligence technology to date:
- how the word is used
- frequency of use
- it is used more often in oral or written speech
- word translation options
- usage examples (several phrases with translation)
- etymology
knot genus - translation to russian
![A Seifert surface bounded by a set of [[Borromean rings]].](https://commons.wikimedia.org/wiki/Special:FilePath/Borromean Seifert surface.png?width=200 "A Seifert surface bounded by a set of [[Borromean rings]].")
![A Seifert surface for the [[Hopf link]]. This is an annulus, not a Möbius strip. It has two half-twists and is thus orientable.](https://commons.wikimedia.org/wiki/Special:FilePath/Hopf band wikipedia.png?width=200 "A Seifert surface for the [[Hopf link]]. This is an annulus, not a Möbius strip. It has two half-twists and is thus orientable.")
математика
род узла
![Egyptian]] statue dating from 2350 BC depicting a reef knot securing a belt](https://commons.wikimedia.org/wiki/Special:FilePath/Egypte louvre 279 couple detail reef knot.jpg?width=200 "Egyptian]] statue dating from 2350 BC depicting a reef knot securing a belt")
![Pontika]] (Ukraine), 300 BC, in the form of a reef knot](https://commons.wikimedia.org/wiki/Special:FilePath/Ancient Greek jewelry Pontika (Ukraina) 300 bC.jpg?width=200 "Pontika]] (Ukraine), 300 BC, in the form of a reef knot")
![Weight for weighing gold dust - Knot – [[MHNT]]](https://commons.wikimedia.org/wiki/Special:FilePath/Akan MHNT.ETH.2010.25.060.jpg ?width=200 "Weight for weighing gold dust - Knot – [[MHNT]]")
['ri:fnɔt]
морской термин
рифовый узел
![pretzel knot]]](https://commons.wikimedia.org/wiki/Special:FilePath/Celtic 7 4 Knot.jpg?width=200 "pretzel knot]]")
![The seven graphs in the [[Petersen family]]. No matter how these graphs are embedded into three-dimensional space, some two cycles will have nonzero [[linking number]].](https://commons.wikimedia.org/wiki/Special:FilePath/Petersen family.svg?width=200 "The seven graphs in the [[Petersen family]]. No matter how these graphs are embedded into three-dimensional space, some two cycles will have nonzero [[linking number]].")
математика
оснащенный узел
Definition
Wikipedia
In mathematics, a Seifert surface (named after German mathematician Herbert Seifert) is an orientable surface whose boundary is a given knot or link.
Such surfaces can be used to study the properties of the associated knot or link. For example, many knot invariants are most easily calculated using a Seifert surface. Seifert surfaces are also interesting in their own right, and the subject of considerable research.
Specifically, let L be a tame oriented knot or link in Euclidean 3-space (or in the 3-sphere). A Seifert surface is a compact, connected, oriented surface S embedded in 3-space whose boundary is L such that the orientation on L is just the induced orientation from S.
Note that any compact, connected, oriented surface with nonempty boundary in Euclidean 3-space is the Seifert surface associated to its boundary link. A single knot or link can have many different inequivalent Seifert surfaces. A Seifert surface must be oriented. It is possible to associate surfaces to knots which are not oriented nor orientable, as well.
