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The Hoxton knot, [1] Chelsea knot, [2] French loop, [3] Parisian scarf knot [4] or Snug Tug [5] is a method of arranging a scarf about the neck. The scarf is doubled back and placed around the neck. The tails of the scarf are then pulled through the U-bend of the doubling to secure them, as with a cow hitch or lark's head.
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 a lay audience, 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.
In other cases, a knot being tied in the bight is a matter of the method of tying rather than a difference in the completed form of the knot. For example, the clove hitch can be made "in the bight" if it is being slipped over the end of a post but not if being cast onto a closed ring, which requires access to an end of the rope.
However, tying the knot this way does not allow putting the loop around a fixed object like a tree; to do that, the knot must be tied in a two-stage process by first tying a figure-eight knot, running the end of the rope around the fixed object, and then threading the rope back through and around the figure-8 knot to create the final figure-8 ...
Emanuel de Geer wearing a military sash over a buff jerkin and sporting a cravat with it in 1656, portrait by Bartholomeus van der Helst. According to 1828 encyclopedic The art of tying the cravat: demonstrated in sixteen lessons, the Romans were the first to wear knotted kerchiefs around their necks, but the modern version of the cravat (French: la cravate) originated in the 1660s.
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