Rubik's CubeDate: 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/ |
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