In the late 1990s, two researchers, Thomas Fink and Yong Mao of Cambridge's Cavendish Laboratory, used mathematical modeling to discover that 85 knots are possible with a conventional tie (limiting the number "moves" used to tie the knot to nine; longer sequences of moves result in too large a knot or leave the hanging ends of the tie too short). The models were published in academic journals, while the results and the 85 knots were published in layman's terms in a book entitled "The 85 Ways to Tie a Tie". Of the 85 knots, Fink and Mao selected 13 knots as "aesthetic" knots, using the qualities of symmetry and balance. Based on these mathematical principles, the researchers came up with not only the four necktie knots in common use, but nine more, some of which had seen limited use, and some that are believed to have been codified for the first time.