# 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) or**Clover 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 of**right hand type

**and**left hand type

**in the three leaf knot as shown in the right figure.**. In other words, it can not be obtained by non-trivial knots.

***Unnamed knot***Reversible**. That is, it is equal regardless of whether it is turned on or off.

***. 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.**. In other words, (the minimum value of the longest upward path in the projection diagram) is 2.

***2 Honbashi knot*****is 2.**of the knot**

*()**(the minimum number of edges required to express as a polygonal knot) is 6.*The number of species**(the smallest of the knot) is 1.**is 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).

**of type (± 2, ± 3) type or (± 3, ± 2) type.*Right hand type****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.**

***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). ApplyingA 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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