CONVERTING A TANGLE INTO A KNOT
Instructions
With a pencil scribble any ‘tangle’ of loops, joining to where you began to form a continuous curve. Regard this as a plan of a ‘knot’ of string.
With a broader felt tip commence tracing this knot anywhere. When you meet the first crossing point make this an ‘over’ by drawing continuously through it.
When you meet the next crossing point make this an ‘under’ by breaking the line you are following either side of the crossing line.
Continue in this manner ‘over’ and ‘under’ alternately, like weaving. Eventually you will meet an existing ‘under’ crossing line with a gap, draw your ‘over’ line through this gap, and continue in the same manner..
Finally you will reach a last crossing, which you will find will be an ‘under’, and you will be able to join onto the start line, which continues as an ’over’.
To leave the finished knot.
The example is a very simple ‘tangle’ -
This apparently simple observation is quite surprising, and has no obvious explanation.
Perhaps a topologist or a knot theorist could comment whether this is a trivial observation or not?