Rubik's Cube

Date: 12/03/98 at 23:19:16
From: S. Smith
Subject: Rubik's cube

I just wanted to know about the Rubik's Cube. Who made it and how it 
can help me learn math? 

Thanks.

Date: 12/04/98 at 12:46:05
From: Doctor Rick
Subject: Re: Rubik's cube

Hi, welcome to Dr. Math's office.

Rubik's Cube was invented in the 1970s by a Hungarian named Erno Rubik. 
Playing with Rubik's Cube makes you think about 3-dimensional shapes, 
visualize what will happen if you turn a face of the cube a certain 
way, and plan ahead. You have to make the cube look worse before it can 
get better, so you can't just do it one step at a time. You learn 
certain patterns - sequences of 3 or 5 or 15 rotations that move the 
little cubes in a certain way. These things are good for stretching 
your mind even if it doesn't seem like math.

A warning, though: it doesn't replace doing homework. The Cube can be
habit-forming, so be careful with it!

There is math in Rubik's Cube that you haven't learned yet. The math 
in Rubik's Cube is a branch of mathematics called Group Theory. Instead 
of multiplying or adding numbers, you rotate faces of the cube, and 
this kind of math helps to describe what happens when you do several 
rotations in a row.

For instance, in regular math, 3 times 2 is 6 and 2 times 3 is also 6. 
But in the "group" that is Rubik's Cube (the set of rules that it 
follows), turning the top counterclockwise and then turning the front 
clockwise is NOT the same as doing these two "operations" in the 
reverse order. We say that the group is not "commutative".

I don't think you'd understand it yet, but in case you'd like to see 
what the math looks like, you could try to find an old copy of 
Scientific American magazine in the library. In March 1981, Douglas 
Hofstadter wrote an article about the mathematics of Rubik's Cube. I 
learned how to solve the Cube by studying this article, but I must 
admit that 9-year-olds with no idea of the math involved could solve 
it faster than I. I have no idea how they did it! 

For another advanced source, this one on the Internet, you could try 
the lecture notes by Professor W. D. Joyner for a class on the 
mathematics of the Rubik's Cube:

   http://web.usna.navy.mil/~wdj/rubik_nts.htm   

- Doctor Rick, The Math Forum
  http://mathforum.org/dr.math/