74 knot

In mathematical knot theory, 7₄ is the name of a 7-crossing knot which can be visually depicted in a highly-symmetric form, and so appears in the symbolism and/or artistic ornamentation of various cultures.

Visual representations

The interlaced version of the simplest form of the Endless knot symbol of Buddhism is topologically equivalent to the 7₄ knot (though it appears to have nine crossings), as is the interlaced version of the unicursal hexagram of occultism. (However, the endless knot symbol has more complex forms not equivalent to 7₄, and both the endless knot and unicursal hexagram can appear in non-interlaced versions, in which case they are not knots at all.)

The 7₄ knot is a Lissajous knot, representable for example by the parametric equation

${\displaystyle {\begin{aligned}x&=\cos(2t+0.22)\\y&=\cos(3t+1.10)\\z&=\cos 7t\end{aligned}}}$

Example

Sources

1. Endless knot
2. Knot theory
3. Trefoil knot
4. Unicursal hexagram
5. Reef knot
6. Molecular knot
7. Knot (mathematics)
8. List of mathematical knots and links
9. Hyperbolic link
10. Prime knot
11. Solomon's knot
12. Conway knot
13. Figure-eight knot (mathematics)
14. Cinquefoil knot
15. Trucker's hitch
16. Torus knot
17. Knot complement
18. 71 knot
19. Chiral knot
20. Unknot