The 85 Ways to Tie a Tie: Difference between revisions
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'''The 85 Ways to Tie a Tie''' (ISBN 1-84115-249-8), by | '''The 85 Ways to Tie a Tie''' (ISBN 1-84115-249-8), by Thomas Fink and [[Yong Mao]], was published by Fourth Estate on Nov 4, 1999, and subsequently published in nine other languages. [[Image:The 85 ways.jpg|thumb|right|The 85 Ways to Tie a Tie]] | ||
==The Book== | == The Book == | ||
'The 85 Ways to Tie a Tie' is about the history of the knotted [[neckcloth]], the modern [[necktie]], and how to tie both. It is based on two mathematics papers published by the same authors in the journal | 'The 85 Ways to Tie a Tie' is about the history of the knotted [[neckcloth]], the modern [[necktie]], and how to tie both. It is based on two mathematics papers published by the same authors in the journal Nature<ref>{{cite journal | last = Fink | first = Thomas M. | authorlink = Thomas Fink | coauthors = and Yong Mao | year = 1999 | title = Designing tie knots by random walks | journal = Nature | volume = 398 | pages = 31–32 | doi = 10.1038/17938}}</ref> and [[Physica D]].{{Fact|date=February 2007}} | ||
The authors prove there are exactly 85 ways of tying a necktie and enumerate them. Of the 85, 13 stand out: the four traditional knots (the [[Four-in-hand knot|four-in-hand]], [[Pratt knot|Pratt]], [[Half-Windsor knot|half-Windsor]] and [[Windsor knot|Windsor]]) and nine others, which the authors name. | The authors prove there are exactly 85 ways of tying a necktie and enumerate them. Of the 85, 13 stand out: the four traditional knots (the [[Four-in-hand knot|four-in-hand]], [[Pratt knot|Pratt]], [[Half-Windsor knot|half-Windsor]] and [[Windsor knot|Windsor]]) and nine others, which the authors name. | ||
==The Science== | == The Science == | ||
The discovery of all possible ways to tie a tie depends on a mathematical formulation of the act of tying a tie. In their papers (which are technical) and book (which is for the layman, apart from an appendix), the authors show that necktie knots are equivalent to persistent random walks on a triangular lattice, with some constraints on how the walks begin and end. Thus enumerating tie knots of n moves is equivalent to enumerating walks of n steps. Imposing the conditions of symmetry and balance reduces the 85 knots to 13 aesthetic ones. | The discovery of all possible ways to tie a tie depends on a mathematical formulation of the act of tying a tie. In their papers (which are technical) and book (which is for the layman, apart from an appendix), the authors show that necktie knots are equivalent to persistent random walks on a triangular lattice, with some constraints on how the walks begin and end. Thus enumerating tie knots of n moves is equivalent to enumerating walks of n steps. Imposing the conditions of symmetry and balance reduces the 85 knots to 13 aesthetic ones. | ||
==Knot Representation== | == Knot Representation == | ||
The basic idea is that tie knots can be described as a sequence of six different possible moves, although not all moves can follow each other. Moreover, there are two ways of beginning a tie knot, and two ways of ending a tie knot. These are summarized as follows. | The basic idea is that tie knots can be described as a sequence of six different possible moves, although not all moves can follow each other. Moreover, there are two ways of beginning a tie knot, and two ways of ending a tie knot. These are summarized as follows. | ||
| Line 19: | Line 19: | ||
T = through the loop just made. | T = through the loop just made. | ||
[[Image: | [[Image:Instruct begin.jpg]] | ||
Above: The two ways of starting a tie knot. | Above: The two ways of starting a tie knot. | ||
[[Image: | [[Image:Instruct moves.jpg]] | ||
Above: The six tie knot moves. | Above: The six tie knot moves. | ||
[[Image: | [[Image:Instruct end.jpg]] | ||
Above: The two ways of finishing a tie knot. | Above: The two ways of finishing a tie knot. | ||
| Line 33: | Line 33: | ||
With this shorthand, traditional and new knots can be compactly expressed as below. | With this shorthand, traditional and new knots can be compactly expressed as below. | ||
==Knots== | == Knots == | ||
The thirteen useful knots (out of 85 total) described in the book, in order of size, are as follows. The knots are sometimes designated by their number alone, e.g., FM2 for the four-in-hand (FM stands for Fink-Mao). | The thirteen useful knots (out of 85 total) described in the book, in order of size, are as follows. The knots are sometimes designated by their number alone, e.g., FM2 for the four-in-hand (FM stands for Fink-Mao). | ||
{| | {| | ||
| Line 63: | Line 63: | ||
|} | |} | ||
==Reviews== | == Reviews == | ||
The book was reviewed in '' | The book was reviewed in ''Nature'',<ref>{{cite journal | last = Buck | first = Gregory | year = 2000 | title = Why not knot right? | journal = Nature | volume = 403 | pages = 362 | doi = 10.1038/35000270}}</ref> ''[[The Daily Telegraph]]'', ''[[The Guardian]]'', ''[[GQ (magazine)|GQ]]'', ''[[Physics World]]'', and others. | ||
==References== | == References == | ||
<!-- See [[Wikipedia:Footnotes]] for instructions. --> | <!-- See [[Wikipedia:Footnotes]] for instructions. --> | ||
<references /> | <references /> | ||
==External links== | == External links == | ||
*[http://www.tcm.phy.cam.ac.uk/~ym101/tie/short/tie_nature4.html Theory of Tie Knots] | *[http://www.tcm.phy.cam.ac.uk/~ym101/tie/short/tie_nature4.html Theory of Tie Knots] | ||
*[http://www.tcm.phy.cam.ac.uk/~tmf20/85ways.shtml The 85 Ways to Tie a Tie at Thomas Fink's homepage] | *[http://www.tcm.phy.cam.ac.uk/~tmf20/85ways.shtml The 85 Ways to Tie a Tie at Thomas Fink's homepage] | ||
[[Category:Necktie knots|85 Ways to Tie a Tie]] | [[Category:Necktie knots|85 Ways to Tie a Tie]] | ||
Latest revision as of 13:48, 6 May 2012
The 85 Ways to Tie a Tie (ISBN 1-84115-249-8), by Thomas Fink and Yong Mao, was published by Fourth Estate on Nov 4, 1999, and subsequently published in nine other languages.
The Book
'The 85 Ways to Tie a Tie' is about the history of the knotted neckcloth, the modern necktie, and how to tie both. It is based on two mathematics papers published by the same authors in the journal Nature[1] and Physica D.[citation needed] The authors prove there are exactly 85 ways of tying a necktie and enumerate them. Of the 85, 13 stand out: the four traditional knots (the four-in-hand, Pratt, half-Windsor and Windsor) and nine others, which the authors name.
The Science
The discovery of all possible ways to tie a tie depends on a mathematical formulation of the act of tying a tie. In their papers (which are technical) and book (which is for the layman, apart from an appendix), the authors show that necktie knots are equivalent to persistent random walks on a triangular lattice, with some constraints on how the walks begin and end. Thus enumerating tie knots of n moves is equivalent to enumerating walks of n steps. Imposing the conditions of symmetry and balance reduces the 85 knots to 13 aesthetic ones.
Knot Representation
The basic idea is that tie knots can be described as a sequence of six different possible moves, although not all moves can follow each other. Moreover, there are two ways of beginning a tie knot, and two ways of ending a tie knot. These are summarized as follows.
L = left; C = centre; R = right.
i = into the page; o = out of the page.
T = through the loop just made.
Above: The two ways of starting a tie knot.
Above: The six tie knot moves.
Above: The two ways of finishing a tie knot.
With this shorthand, traditional and new knots can be compactly expressed as below.
Knots
The thirteen useful knots (out of 85 total) described in the book, in order of size, are as follows. The knots are sometimes designated by their number alone, e.g., FM2 for the four-in-hand (FM stands for Fink-Mao).
| 1. | Lo Ri Co T | Small knot |
| 2. | Li Ro Li Co T | Four-in-hand |
| 3. | Lo Ri Lo Ri Co T | Kelvin |
| 4. | Lo Ci Ro Li Co T | Nicky (self-releasing Pratt) |
| 5. | Lo Ci Lo Ri Co T | Pratt knot |
| 6. | Li Ro Li Ro Li Co T | Victoria |
| 7. | Li Ro Ci Lo Ri Co T | Half-Windsor knot |
| 12. | Lo Ri Lo Ci Ro Li Co T | St Andrew |
| 18. | Lo Ci Ro Ci Lo Ri Co T | Plattsburgh |
| 23. | Li Ro Li Co Ri Lo Ri Co T | Cavendish |
| 31. | Li Co Ri Lo Ci Ro Li Co T | Windsor knot |
| 44. | Lo Ri Lo Ri Co Li Ro Li Co T | Grantchester |
| 54. | Lo Ri Co Li Ro Ci Lo Ri Co T | Hanover |
Reviews
The book was reviewed in Nature,[2] The Daily Telegraph, The Guardian, GQ, Physics World, and others.
References
- ↑ Fink, Thomas M.; and Yong Mao (1999). "Designing tie knots by random walks". Nature 398: 31–32. doi:10.1038/17938.
- ↑ Buck, Gregory (2000). "Why not knot right?". Nature 403: 362. doi:10.1038/35000270.
