Knots, tangles, braids, and rational numbers

The subject of knot theory concerns the phenomena of “knotting”, “tangling”, and “braiding”, investigated from a mathematical point of view. I’ll discuss a family of tangles called rational tangles and the related concepts of 2-bridge knots and plat closures of 4-braids. Rational tangles are named after John Conway’s remarkable classification of them: they admit a natural one-to-one correspondence with the rational numbers (and infinity).