The necktie (or tie) is a long piece of cloth worn around the neck. It rests under the shirt collar and is knotted at the throat. The modern necktie, ascot, and bow tie, descended from the cravat. Men and women (to a far lesser extent) wear neckties as part of regular office attire, formal wear, or uniforms. Neckties are also worn as part of a uniform (e.g. military, school, wait staff). Variants include the bow tie, ascot tie, bola tie, and the clip-on tie.------------After the Second World War, hand-painted ties became an accepted form of decoration in America. The widths of some of these ties went up to 4.5 inches. These loud, flamboyant ties sold very well all the way through the 1950s. On the other side of the pond, Regimental stripes have been continuously used in tie designs since the 1920s. Traditionally, English stripes ran from the left shoulder down to the right side; however, when Brooks Brothers introduced the striped ties in the States a century ago, they had theirs cut in the opposite direction. The 1960s brought about an influx of pop art influenced designs. The first was designed by Michael Fish when he worked at Turnbull & Asser. The term kipper, was a pun on his name. The exuberance of the styles of the late 1960s and early 1970s gradually gave way to more restrained designs. Ties became narrower, returning to their 2-3 inch width with subdued colours and motifs, traditional designs of the 1930s and 1950s reappeared, particularly Paisley patterns. Ties began to be sold along with shirts and designers slowly began to experiment with bolder colours. This grew till the 1980s and 1990s where there developed a taste for increasingly unusual designs. There was an increased number of deliberately kitsch designs and joke ties. These ties were often made of plastic or even wood and were more statement pieces than fashion.-------------------The clip-on necktie is permanently knotted bow tie or four-in-hand style affixed with a metal clip to the front of the shirt collar. This 20th-century innovation is considered by some to be stylistically inferior, but may be considered by some for wear in occupations (e.g., law enforcement, service clerks, airline pilots, engineers etc.) where a proper necktie could pose a choking risk in the course of doing his or her job.--------------There are four main knots used to knot neckties. The simplest, the four-in-hand knot, may be the most common. The others (in order of difficulty) are: * the Pratt knot (the Shelby knot) * the half-Windsor knot * the Windsor knot (also erroneously called the "double-Windsor"). The Windsor knot is the thickest knot of the four, since its tying has the most steps. The Windsor knot is named after the Duke of Windsor, although he neither invented nor used it. The Duke did favour a voluminous knot; however, he achieved such by having neckties specially made of thicker cloths. In the late 1990s, two researchers, Thomas Fink and Yong Mao of Cambridge's Cavendish Laboratory, used mathematical modelling to discover that eighty-five (85) knots are possible with a conventional tie (limiting the number of moves to nine).