Last modified 10 December, 2006.

The 85 Ways to Tie a Tie

The The 85 Ways to Tie a Tie refers to both the number of knots that can be tied in a conventional necktie, and a popular book on the history and science of ties and tie knots.

The book grew out of two journal articles by myself and Yong Mao, in which we introduced a mathematical respresentation of tie knots and proved that, with a conventional necktie, there are exactly 85 possible ways to tie it. Of these, just over a dozen are sufficiently handsome or different from each other to be worn. These include the four traditional knots - the four-in-hand, the Nicky (a derivative of the Pratt knot), the half-Windsor and the Windsor - and a number of previously unknown knots.

Classic Knot Tables
Links and Books
A Brief Tour


The 85 Ways to Tie a Tie, small cover
Paperback, 144 pp., (Thomas Fink and Yong Mao), published 2001 by Fourth Estate

The book itself studies the history of the knotted neckcloth, introduces some elementary notions from topology, and gives an overview of the 85 knots and the history of those previously discovered. The 85 Ways has been published in English (UK and America), French, German, Spanish, Portugese, Italian, Dutch and Japanese.

Further details, reviews and sales can be found on
and .
Wikipedia has a page on the book here.


The Guardian As I recline weekly in velvet smoking jacket and exquisite cravat to dictate The List to my oiled, submissive stenographer, it is often given to me to muse on the science and aesthetics of tie knots. Happily, Messrs Fink and Mao have now systematized the study of this most indispensable of gentlemen's apparel. Our authors are Cambridge physicists, and they have devised a highly ingenious mathematical method of proving exactly how many different ways there are to tie a tie, given certain practical (tie length, volume of knot) and aesthetic (symmetry) constraints. Such an advance in our understanding is the fruit of knot theory, a branch of topology under which we can see that a tie is a random walk on a triangular lattice. This eminently desirable little volume also paints a deft history of the tie, with clear knotting diagrams for each of its sartorial results. A perfect seasonal gift for fathers who would like to enter the new millennium more sprightly of step, and more elegant of neck.

Nature (for full review view pdf) This wonderful little book by Thomas Fink and Yong Mao has changed my life. Now, when I tie a tie, I know what I am doing, and why. Fink and Mao have performed a great service for civilization, doing for tie-knot tying what Isaac Newton did for the motion of the heavens: lifting it from the darkness of secrecy, ritual and superstition to the light of rational, scientific good taste...Fink and Mao have shown that it's possible to be both smart and smart - in brains and style.

The Independent A masterpiece of ludicrous arcana by two Cambridge researchers....

Physics World It's a brilliant idea for a book. Thomas Fink and Yong Mao are condensed-matter theorists at the Cavendish Laboratory, Cambridge, and their work on tying knots made headlines around the world last year after it was published in Nature (1999, 398, 31). Using ideas from statistical mechanics, they worked out that there are 85 ways to tie a necktie. However, only 13 of these knots were deemed to be aesthetic on the grounds of "symmetry" and "balance". Three of these - the Windsor, the half-Windsor and the four-in-hand - were already widely known, whilst a fourth, dubbed the Nicky, was found to be a simpler version of the unaesthetic "Pratt", which was invented to much acclaim in 1989.

GQ The fact that only thirteen knots withstood their aesthetic contraints is comparatively unimportant. More interestingly the authors accompany it with a deft but resolute history of the tie, as well as detailed knotting instructions. The unconventional should consider one of the rather novel options like the "crossed Christensen". But perhaps not before the office, it might take some time.

The Telegraph Once they have established the history, the authors explain their knotting breakthrough. Mathematicians have already invented a rich and precise language for each element of knotting, and Fink and Mao combine these elements in all possible ways to create a rich array of knots. They also show how to exploit mathematical rules in order to define when a knot is distinct from anything that has ever been seen before...


The book was inspired by two papers. The first gives a summary of our principal results; the second, uncut version contains all the mathematical details.

Thomas M. Fink and Yong Mao,
`Designing Tie Knots Using Random Walks',
Nature, 398, 31 (1999).   pdf

The simplest of conventional tie knots, the Four-in-Hand, has its origins in late nineteenth-century England. The Duke of Windsor, after abdicating in 1936, has been credited with introducing what is now known as the Windsor knot, whence its smaller derivative, the Half-Windsor, evolved. More recently, in 1989, the Pratt knot was revealed on the front page of the New York Times, the first new knot to appear in 50 years.
      Rather than wait another half-century for the next sartorial advance, here we present a more formal approach. We introduce a mathematical model of tie knots and provide a map between tie knots and persistent random walks on a triangular lattice. We classify knots according to their size and shape and quantify the number of knots in each class. The optimal knot in a class is selected by the proposed aesthetic conditions of symmetry and balance. Of the 85 knots which can be tied with a conventional tie, we recover the four knots in widespread use and introduce six new aesthetic ones.

Thomas M. Fink and Yong Mao,
`Tie Knots, Random Walks and Topology',
Physica A, 276, 109 (2000). pdf

In 1999 the Institute of Physics declared the authors' work as one of the top 10 physics highlights of the year.

Classic Knot Tables

Links and Books

On the Web

Knots on the Web   (on knots) Peter Suber's web page design is also noteworthy.
Necktie Knots   (on tie knots) Part of Peter Suber's Knots on the Web.
Tie Yourself in Knots   (on ties) Many links.
Knot Plot   (on knots) Lots of knot pictures.


Clifford W. Ashley, The Ashley Book of Knots (Faber and Faber, London, 1944. Reissued by Doubleday, New York, 1993.
Colin C. Adams, The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots (Freeman and Co., New York, 1994).
Charles Livingston, Knot Theory (Mathematical Association of America, Washington, 1993).

Tie Knots

Anonymous, Neckclothitania; or, Tietania (J. J. Stockdale, London, 1818).
H. Le Blanc, The Art of Tying Cravats (Effingham Wilson, London, 1828).
Davide Mosconi and Riccardo Villarosa, Getting Knotted (Ratti, Milan, 1985). Republished as The Book of Ties (Tie Rack, London, 1985).


Francois Chaille, The Book of Ties (Flammarion, Paris, 1996).
Doriece Colle, Collars, Stocks, Cravats (Rodale Press, Emmaus, PA, 1972).
Roseann Ettinger, 20th Century Neckties (Schiffer Publishing, Atglen, PA, 1998).
Sarah Gibbings, The Tie (Studio Editions, London, 1990).
Avril Hart, Ties (Victoria & Albert Museum, London, 1998).
A. Varron, `Neckties', Ciba Review, 38, 1361 (1941).

Men's Dress

Hardy Amies, The Englishman's Suit (Quartet, London, 1994).
A Cavalry Officer, The Whole Art of Dress (Effingham Wilson, London, 1830).
Farid Chenoune, A History of Men's Fashion, (Flammarion, New York, 1993).
C. Willet Cunnington and Phillis Cunnington, Handbook of English Costume in the 19th Century (Faber and Faber, London, 1959).
Alan Flusser, Clothes and the Man (Villard, New York, 1988). Extract on ties.
Clare Jerrold, The Beaux and the Dandies (Stanley Paul & Co., London, 1910).
James Laver, Dandies (Weidenfeld and Nicolson, London, 1968).
The `Major' of To-Day, Clothes and the Man (Grant Richards, London, 1900).
Alan Mansfield and Phillis Cunnington, Handbook of English Costume in the 20th Century, 1900-1950 (Faber and Faber, London, 1973).
Aileen Ribeiro and Valerie Cumming, The Visual History of Costume, (Batsford Ltd, London, 1989).
O. E. Schoeffler and W. Gale, Esquire's Encyclopedia of 20th Century Men's Fashion (McGraw-Hill, New York, 1973).
The Duke of Windsor, A Family Album (Cassell, London, 1960).

A Brief Tour

My favourite review from

Hey, guys.  Have you ever wanted to know the origins of the necktie you wear to work every day?  Me neither.  But I do now, thanks to a book called The 85 Ways to Tie a Tie, written by Thomas Fink and Yong Mao.

Before we get into all that, you've got to see this ad, which I scanned from the book:


Boy, get a load of this, willya?  This is from 1951, which isn't really that long ago.  God knows why the guy is wearing a tie in bed, but it seems to be doing the trick.  Smug bastard.

Van Heusen is still in business, I believe, but I somehow don't think this line of reasoning works these days.

The book is chock full of information about ties.  I mean, CHOCK full.  For instance, I bet you think the first neckties were worn by Roman soldiers, don't you?  I bet you go on and on about it, never shutting up about the Romans and their ties.  Well, you're wrong.  In 1974, the tomb of China's first emperor, Qin Shih-huang-di (pronounced noo-yen) was uncovered, along with an army of over 7,000 terracotta soldiers.  And what were these soldiers wearing?  Around their necks?  Give up?

Yep, a necktie.  Type thing.  Sorta.  And this was way back in about 250 B.C.

After the Chinese and Romans got done with them, the necktie went to France, where it was adopted by "dandies."  After that it went to England, where it got really frilly and ridiculous looking.  That is, until some guy defeated some people or something.  I don't know, it's all in the book.  The result of this was the ties stopped being frilly and started being knotty.

There is an overwhelming amount of information about knots, knot tying, knot science, knot history, and knot theory in this book.  Think I'm kidding?

In order for you to know how to tie all these 85 different knots, you first have to learn all the different moves:

Then follow this table:

And study these figures...

...master these fomulas:

Oh, and a few diagrams...


Or, just tie a pair of pants around your neck, like this guy did.

(Thanks to Nikki for getting me this book, which is actually pretty darn cool.  Sure, Nikki is a woman, but she knows more about football and baseball than most guys I know, so it's not too much of an intrusion in our week of testosterone to give her a mention.  Thanks!)

Thomas Fink

Home           Contact           About me           About my page           FAQ

Popular Page

chaps, cads, blokes and bounders


What's New
The Man's Book
The 85 Ways to Tie a Tie
Some Links of Note