From Scientific American
New ways of tying a necktie appear rarely. Some 50 years passed between the introduction of the Windsor knot and the arrival of the Pratt knot in 1989. "Rather than wait another half-century for the next knot," Fink and Mao write, "we considered a more formal approach." And so they present 85 tie-tying techniques, each one shown in a drawing with instructions on how to achieve the desired result. They also offer a brief history of neckwear and photographs of famous figures wearing ties, among them Fred Astaire in a four-in-hand, Frank Sinatra in a Windsor knot and the Duke of Windsor not wearing a Windsor. But, being research physicists at the University of Cambridge, the authors are interested in more than sartorial versatility. They deal also with knot theory and topology. For the reader who wishes to probe tie-tying that deeply, they represent "knot sequences as random walks on a triangular lattice."
EDITORS OF SCIENTIFIC AMERICAN
"In an elegant world, an irreproachable tie knot is an essential part of one's toilette; it does not matter whether the knot is simple or complicated, because the art is what counts. There are some knots which seem casual in appearance, but which have taken considerable labour before the mirror, and many a stamped foot, many an exclamation of impatience."
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-- Doctor A. Debray Hygiene Vestimentaire, 1857