(Q168697)

English

figure-eight knot

unique knot with a crossing number of four

Listing's knot
4_1
4₁
4a_1
Figure-eight

In more languages

default for all languages

No label defined

No description defined

edit

Statements

0 references

0 references

0 references

0 references

Blue Figure-Eight Knot.png
1,584 × 1,800; 537 KB

0 references

name

Listing's knot (English)

named after

Johann Benedict Listing

0 references

figure-eight knot (English)

0 references

defining formula

{\begin{pmatrix}x\\y\\z\end{pmatrix}}={\begin{pmatrix}\left(2+\cos {(2t)}\right)\cos {(3t)}\\\left(2+\cos {(2t)}\right)\sin {(3t)}\\\sin {(4t)}\end{pmatrix}}

1 reference

imported from Wikimedia project

German Wikipedia

3D model

Achterknoten 20230608 001.stl
5,120 × 2,880; 43.33 MB

0 references

maintained by WikiProject

WikiProject Mathematics

0 references

crossing number

4

0 references

Alexander polynomial

-t+3-t^{-1}

0 references

Conway polynomial

1-z^{2}

0 references

Jones polynomial

q^{2}-q+1-q^{-1}+q^{-2}

0 references

Alexander–Briggs notation

4_{1}

0 references

Dowker-Thistlethwaite notation

4,6,8,2

0 references

Dowker-Thistlethwaite name

4a_{1}

0 references

Gauss notation

\{-1,2,-3,1,-4,3,-2,4\}

0 references

Commons category

Figure-eight knots (knot theory)

0 references

Identifiers

1 reference

28 October 2013

0 references

0 references

1 reference

imported from Wikimedia project

English Wikipedia

Microsoft Academic ID

2777989480

0 references

Sitelinks

Wikipedia(9 entries)

Wikibooks(0 entries)

Wikinews(0 entries)

Wikiquote(0 entries)

Wikisource(0 entries)

Wikiversity(0 entries)

Wikivoyage(0 entries)

Wiktionary(0 entries)

Multilingual sites(1 entry)

commonswiki Category:Figure-eight knots (knot theory)