figure-eight knot

Summary

figure-eight knot is a prime knot^[1]. It ranks in the top 10% of prime_knot entities by monthly Wikipedia readership (163 views/month).^[2]

Key Facts

• figure-eight knot's image is recorded as Blue Figure-Eight Knot.png^[3].
• figure-eight knot's instance of is recorded as prime knot^[4].
• figure-eight knot's instance of is recorded as alternating knot^[5].
• figure-eight knot's instance of is recorded as fibered knot^[6].
• figure-eight knot's instance of is recorded as twist knot^[7].
• figure-eight knot's Commons category is recorded as Figure-eight knots (knot theory)^[8].
• figure-eight knot's Freebase ID is recorded as /m/0g6v3^[9].
• figure-eight knot's defining formula is recorded as \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}^[10].
• figure-eight knot's name is recorded as {'lang': 'en', 'text': "Listing's knot"}^[11].
• figure-eight knot's name is recorded as {'lang': 'en', 'text': 'figure-eight knot'}^[12].
• figure-eight knot's MathWorld ID is recorded as FigureEightKnot^[13].
• figure-eight knot's 3D model is recorded as Achterknoten 20230608 001.stl^[14].
• figure-eight knot's Alexander polynomial is recorded as -t + 3 - t^{-1}^[15].
• figure-eight knot's Conway polynomial is recorded as 1-z^2^[16].
• figure-eight knot's Jones polynomial is recorded as q^2 - q + 1 - q^{-1} + q^{-2}^[17].
• figure-eight knot's maintained by WikiProject is recorded as WikiProject Mathematics^[18].
• figure-eight knot's Microsoft Academic ID is recorded as 2777989480^[19].
• figure-eight knot's Alexander–Briggs notation is recorded as 4_1^[20].
• figure-eight knot's Dowker-Thistlethwaite notation is recorded as 4, 6, 8, 2^[21].
• figure-eight knot's Dowker-Thistlethwaite name is recorded as 4a_{1}^[22].
• figure-eight knot's Knot Atlas ID is recorded as 4_1^[23].
• figure-eight knot's Knotinfo ID is recorded as 4_1^[24].
• figure-eight knot's Gauss notation is recorded as {-1, 2, -3, 1, -4, 3, -2, 4}^[25].
• figure-eight knot's crossing number is recorded as {'amount': '+4'}^[26].
• figure-eight knot's Great Russian Encyclopedia portal ID is recorded as uzel-listinga-1da1d6^[27].

Why It Matters

figure-eight knot ranks in the top 10% of prime_knot entities by monthly Wikipedia readership (163 views/month).^[2] It has Wikipedia articles in 8 language editions, a strong signal of global cultural recognition.^[28] It is known by 18 alternative names across languages and contexts.^[29]