Three leaf knot

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(Right hand type) three leaf knot

Minimum intersection point of right-handed trifolious knot

Minimum intersection projection of left-handed trifolious knot

Three Leaf Knot(Miyubo Muibu / Mitsuba Muibu, Trefoil knot) orClover Knot Is the most simple knot not obvious in a field of. It corresponds to what I call it.

The origin of the name is. There are plenty of designs treated with a three leaf knot, for example, the department of mathematics depicts the trifolious knotted sculpture created by the department as a symbol of the department.

Nature of three leaves knot

Not a two handed knot*. That is, it is not equal to. Therefore, exactly there are two kinds ofright hand typeandleft hand typein the three leaf knot as shown in the right figure. Reversible*. That is, it is equal regardless of whether it is turned on or off. *Unnamed knot. In other words, it can not be obtained by non-trivial knots. *. In other words, we have an alternate projection map (both projection projections on the right figure are alternating projections). (the minimum value of the number of intersection points in the projection map) is 3. There are no knots with 3 intersections other than the three leaf knot. (the minimum number of cross-exchanges required to solve a knot) is one. *is 2. *2 Honbashi knot. In other words, (the minimum value of the longest upward path in the projection diagram) is 2. ()(the minimum number of edges required to express as a polygonal knot) is 6. The number of speciesof the knot(the smallest of the knot) is 1. *of type (± 2, ± 3) type or (± 3, ± 2) type. Right hand typeis t - 1 + t - 3 - t - 4 {\ displaystyle t ^ {- 1} + t ^ {- 3} - t ^ {- 4}}! [{\ \ Displaystyle t ^ {-1} + t ^ {-3} - t ^ {-4}}] (https://wikimedia.org/api/rest_v1/media/math/render/svg/2bc55aa3a233b2c32085347501ff8ba249709d50), the left hand type is t + t 3 - t 4 {\ displaystyle t + t ^ {3} - t ^ {4}}! {{\ displaystyle t + t ^ {3} - t ^ {4}}] (https: //wikimedia .org / api / rest_v1 / media / math / render / svg / d9a60b 8184152d669de90b5b6b655342b1224872). *is left hand type right hand type t - 1 - 1 + t {\ displaystyle t ^ {- 1} - 1 + t}! {{\ Displaystyle t ^ {- 1} - 1 + t} ] (https://wikimedia.org/api/rest_v1/media/math/render/svg/615be96efb94d005411e6a9050a203d43668b6e7). Applying**with a coefficient of 1 along the right-handed trilobal knot to * yields: The same is true for surgery with a coefficient of -1 on the left hand side.

A gallery

Editing "Three Leaf Knot" - - | | | | | |

References

• Author, translation "Mathematics of knot", 1998. .
• "Knot theory and its application", 1993. .
• V. V. Prasolov, A. B. Sossinsky, _ Knots, Links, Braids and 3 - Manifolds, Amer Mathematical Society, 1993.

1. ****Clifford · A. · Pickover "Mobius Zone" Yoshida Kichinagari translation, company, 2007, p. 37. .

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Post Date : 2018-02-07 09:30

This article is taken from the Japanese Wikipedia Three leaf knot

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