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List Of Prime Knots
In knot theory, prime knots are those knots that are indecomposable under the operation of knot sum. The prime knots with ten or fewer crossings are listed here for quick comparison of their properties and varied naming schemes. Table of prime knots Six or fewer crossings Seven crossings Eight crossings Nine crossings Ten crossings Higher *Conway knot 11n34 *Kinoshita–Terasaka knot 11n42 Table of prime links Seven or fewer crossings Higher See also * List of knots This list of knots includes many alternative names for common knots and lashings. Knot names have evolved over time, and there are many conflicting or confusing naming issues. The overhand knot, for example, is also known as the thumb knot. The ... * List of mathematical knots and links * Knot tabulation * (−2,3,7) pretzel knot Notes External links * KnotInfo, ''Indiana.edu''. {{DEFAULTSORT:Prime knots Knot theory Mathematics-related lists ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Knot Theory
In the mathematical field of topology, knot theory is the study of mathematical knots. While inspired by knots which appear in daily life, such as those in shoelaces and rope, a mathematical knot differs in that the ends are joined so it cannot be undone, the simplest knot being a ring (or "unknot"). In mathematical language, a knot is an embedding of a circle in 3-dimensional Euclidean space, \mathbb^3 (in topology, a circle is not bound to the classical geometric concept, but to all of its homeomorphisms). Two mathematical knots are equivalent if one can be transformed into the other via a deformation of \mathbb^3 upon itself (known as an ambient isotopy); these transformations correspond to manipulations of a knotted string that do not involve cutting it or passing through itself. Knots can be described in various ways. Using different description methods, there may be more than one description of the same knot. For example, a common method of describing a knot is a planar d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stevedore Knot (mathematics)
In knot theory, the stevedore knot is one of three prime knots with crossing number six, the others being the 62 knot and the 63 knot. The stevedore knot is listed as the 61 knot in the Alexander–Briggs notation, and it can also be described as a twist knot with four twists, or as the (5,−1,−1) pretzel knot. The mathematical stevedore knot is named after the common stevedore knot, which is often used as a stopper at the end of a rope. The mathematical version of the knot can be obtained from the common version by joining together the two loose ends of the rope, forming a knotted loop. The stevedore knot is invertible but not amphichiral. Its Alexander polynomial is :\Delta(t) = -2t+5-2t^, \, its Conway polynomial is :\nabla(z) = 1-2z^2, \, and its Jones polynomial is :V(q) = q^2-q+2-2q^+q^-q^+q^. \, The Alexander polynomial and Conway polynomial are the same as those for the knot 946, but the Jones polynomials for these two knots are different. B ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
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.) File:EndlessKnot03d.png, One form of the Endless knot of Buddhism File:Interwoven unicursal hexagram.svg, Interwoven unicursal hexagram. File:Celtic-knot-linear-7crossings.svg, 74 knot in Celtic artistic form, also found in some Hausa embroideries.''Celtic Art: The Methods of Construction'' by George Bain, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
7 2 Knot
7 (seven) is the natural number following 6 and preceding 8. It is the only prime number preceding a cube. As an early prime number in the series of positive integers, the number seven has greatly symbolic associations in religion, mythology, superstition and philosophy. The seven Classical planets resulted in seven being the number of days in a week. It is often considered lucky in Western culture and is often seen as highly symbolic. Unlike Western culture, in Vietnamese culture, the number seven is sometimes considered unlucky. It is the first natural number whose pronunciation contains more than one syllable. Evolution of the Arabic digit In the beginning, Indians wrote 7 more or less in one stroke as a curve that looks like an uppercase vertically inverted. The western Ghubar Arabs' main contribution was to make the longer line diagonal rather than straight, though they showed some tendencies to making the digit more rectilinear. The eastern Arabs develope ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Blue 7 2 Knot
Blue is one of the three primary colours in the RYB colour model (traditional colour theory), as well as in the RGB (additive) colour model. It lies between violet and cyan on the spectrum of visible light. The eye perceives blue when observing light with a dominant wavelength between approximately 450 and 495 nanometres. Most blues contain a slight mixture of other colours; azure contains some green, while ultramarine contains some violet. The clear daytime sky and the deep sea appear blue because of an optical effect known as Rayleigh scattering. An optical effect called Tyndall effect explains blue eyes. Distant objects appear more blue because of another optical effect called aerial perspective. Blue has been an important colour in art and decoration since ancient times. The semi-precious stone lapis lazuli was used in ancient Egypt for jewellery and ornament and later, in the Renaissance, to make the pigment ultramarine, the most expensive of all pigments. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
71 Knot
In knot theory, the 71 knot, also known as the septoil knot, the septafoil knot, or the (7, 2)-torus knot, is one of seven prime knots with crossing number seven. It is the simplest torus knot after the trefoil and cinquefoil. Properties The 71 knot is invertible but not amphichiral. Its Alexander polynomial In mathematics, the Alexander polynomial is a knot invariant which assigns a polynomial with integer coefficients to each knot type. James Waddell Alexander II discovered this, the first knot polynomial, in 1923. In 1969, John Conway showed a ... is :\Delta(t) = t^3 - t^2 + t - 1 + t^ - t^ + t^, \, its Conway polynomial is :\nabla(z) = z^6 + 5z^4 + 6z^2 + 1, \, and its Jones polynomial is :V(q) = q^ + q^ - q^ + q^ - q^ + q^ - q^. \, Example See also * Heptagram References {{DEFAULTSORT:7 1 knot ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Blue 7 1 Knot
Blue is one of the three primary colours in the RYB colour model (traditional colour theory), as well as in the RGB (additive) colour model. It lies between violet and cyan on the spectrum of visible light. The eye perceives blue when observing light with a dominant wavelength between approximately 450 and 495 nanometres. Most blues contain a slight mixture of other colours; azure contains some green, while ultramarine contains some violet. The clear daytime sky and the deep sea appear blue because of an optical effect known as Rayleigh scattering. An optical effect called Tyndall effect explains blue eyes. Distant objects appear more blue because of another optical effect called aerial perspective. Blue has been an important colour in art and decoration since ancient times. The semi-precious stone lapis lazuli was used in ancient Egypt for jewellery and ornament and later, in the Renaissance, to make the pigment ultramarine, the most expensive of all pigments. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Blue 6 3 Knot
Blue is one of the three primary colours in the RYB colour model (traditional colour theory), as well as in the RGB (additive) colour model. It lies between violet and cyan on the spectrum of visible light. The eye perceives blue when observing light with a dominant wavelength between approximately 450 and 495 nanometres. Most blues contain a slight mixture of other colours; azure contains some green, while ultramarine contains some violet. The clear daytime sky and the deep sea appear blue because of an optical effect known as Rayleigh scattering. An optical effect called Tyndall effect explains blue eyes. Distant objects appear more blue because of another optical effect called aerial perspective. Blue has been an important colour in art and decoration since ancient times. The semi-precious stone lapis lazuli was used in ancient Egypt for jewellery and ornament and later, in the Renaissance, to make the pigment ultramarine, the most expensive of all pigments. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
63 Knot
In knot theory, the 63 knot is one of three prime knots with crossing number six, the others being the stevedore knot and the 62 knot. It is alternating, hyperbolic, and fully amphichiral. It can be written as the braid word :\sigma_1^\sigma_2^2\sigma_1^\sigma_2. \, Symmetry Like the figure-eight knot, the 63 knot is fully amphichiral. This means that the 63 knot is amphichiral, meaning that it is indistinguishable from its own mirror image. In addition, it is also invertible, meaning that orienting the curve in either direction yields the same oriented knot. Invariants The Alexander polynomial of the 63 knot is :\Delta(t) = t^2 - 3t + 5 - 3t^ + t^, \, Conway polynomial is :\nabla(z) = z^4 + z^2 + 1, \, Jones polynomial is :V(q) = -q^3 + 2q^2 - 2q + 3 - 2q^ + 2q^ - q^, \, and the Kauffman polynomial is :L(a,z) = az^5 + z^5a^ + 2a^2z^4 + 2z^4a^ + 4z^4 + a^3z^3 + az^3 + z^3a^ + z^3a^ - 3a^2z^2 - 3z^2a^ - 6z^2 - a^3z - 2az - 2za^ - za^-3 + a^2 + a^ +3. \, The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
