MATHS BITE: Reidemeister Moves

In the 1930s, Kurt Reidemeister proved that there are knots that exist which are different from the unknot:

Image result for unknot
Unknot | Source: Wikipedia

He did this by showing that two knot diagrams belong to the same type of knot if they can be related by a sequence of three Reidemeister moves:

  1. Twist and untwist in either direction;
  2. Move one loop completely over another;
  3. Move a string completely under a crossing.


Reidemeister Moves | Source: Wolfram MathWorld

This was an extremely important result in knot theory. One important context in which these moves appear is to define knot invariants: by demonstrating that a property of a knot is unchanged after applying any of the Reidemeister moves, an invariant is defined.

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