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.

 

ReidemeisterMoves_1001.gif

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.

M x

 

Advertisements

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s