Fun group theory stuff mixed in with Baez Week 228

[Martin]

the mathematician john baez has an online blog-like column with some entertaining math facts and often some surprisingly beautiful pictures

 

here is the latest "Week" #228 (he doesnt write them every week, only now and then)

 

http://math.ucr.edu/home/baez/week228.html

 

there is a math trick you can do with the ISBN number of any book

(involves numbers MOD 11, so there is a bit of algebra)

(or if you think of adding numbers mod 11 as group theory then it has a bit of that)

 

and more interesting, there is a game that two people can play with two pieces of rope

 

It involves "rational" tangles or knots, and a number system that describes the knots

 

the game is very simple but the fact that it works, to prove this, the proof involves the socalled Jones polynomial, so it is a simple game of tangling and untangling rope but there is some interesting knot-theory underlying it.