Archaeologists have discovered that knot tying dates back to prehistoric times. Besides their uses such as recording information and tying objects together, knots have interested … 展开

A useful way to visualise and manipulate knots is to project the knot onto a plane—think of the knot casting a shadow on the wall. A small change in the direction of projection will ensure … 展开

A knot invariant is a "quantity" that is the same for equivalent knots (Adams 2004) (Lickorish 1997) (Rolfsen 1976). For example, if the invariant is … 展开

A knot in three dimensions can be untied when placed in four-dimensional space. This is done by changing crossings. Suppose one strand is behind another as seen from a chosen point. Lift it into the fourth dimension, so there is no obstacle (the front strand having … 展开

A knot is created by beginning with a one-dimensional line segment, wrapping it around itself arbitrarily, and then fusing its two free ends together to form a closed loop (Adams 2004) … 展开

Two knots can be added by cutting both knots and joining the pairs of ends. The operation is called the knot sum, or sometimes the connected … 展开

Traditionally, knots have been catalogued in terms of crossing number. Knot tables generally include only prime knots, and only one entry for a knot and its mirror image (even if they are … 展开