Is it a

knot, or

not a knot? Reidermeister moves help you resolve such a dilemma. Mathematical knots can be rather deceitful when they're

complicated. What looks like a knot may in fact be an unknot. It may be possible to untangle the thing until it becomes a perfect loop, an unknot. It is quite difficult to tell just by visualizing the questionable knot. One way of determining its knotishness is by making a

physical model of it and tugging away until you're out of ideas. Another way is to make a

2-dimensional projection of the knot (its

shadow) and examine the crossings. When untangling a pseudo-knot, there are three possible moves that could eventually give you an unknot. These moves are called Reidemeister moves. They look somewhat like this:

**Move 1:**

|*********

|*********

|**/----\**

\*/*****\*

*\******|*

/*\*****/*

|**\----/**

|**********

|**********

to

|.....

|.....

\.....

.\....

..\...

...|..

../...

./....

|.....

|.....

Note that at the end of this move, the string is slightly twisted, but the strings that mathematical knots are made of are 1-dimensional threads and so are infinately stretchy!

**Move 2:**

|.....|.....

|.....|.....

.\....|.....

..\--|-....

......|..\..

......|...\.

......|...|.

......|../..

../--|-....

./....|.....

/.....|.....

|.....|.....

|.....|.....

to

|...|

|...|

|...|

|...|

|...|

|...|

Note that the curved string is under the straight string, it does not cross over.

**Move 3:**
\.|....../.

.\.\..../..

..\.\../...

...\.\/....

....\/\....

..../\.\...

.../..\/...

../.../\...

./.../..\..

/.../....\.

to

\.|....../.

.\|...../..

..\..../...

..|\../....

..|.\/.....

..|./\.....

..|/..\....

../....\...

./|.....\..

/.|......\.

Note again that the single (eventually) straight string is crossing under the two diagonal strings, so it can be shifted over with ease.

Here comes the best part: Any unknot will **at most** take 2^(100,000,000,000*n*) Reidemeister moves to untangle, where *n* is the number of times the string crosses itself.

Go try it on your own impossibly complicated pseudo-knot today!