Timeline for Cool problems to impress students with group theory
Current License: CC BY-SA 2.5
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 31, 2011 at 16:33 | comment | added | ADL | I quite like the fact that one can apply a sequence of arbitrary moves (aka an arbitrary group element) a finite number of times to get back to where you started from (because, of course, every element in your group has finite order). This is quite easy to demonstrate (given finite time...) It is also trivial (but interesting!) to note that there is no single sequence of moves (aka group element) which will take any position and return it to the `solved' cube. This is basically asking if your group is cyclic, and it obviously isn't. | |
| Jan 29, 2010 at 8:03 | comment | added | aorq | Well, the standard fact is that if you break the cube up into pieces and reassemble, the probability that you can get back to the proper configuration is 1/12. There are two factors of 1/2 from standard even/odd permutation considerations, while the last 1/3 comes from a Z/3Z invariant. | |
| Jan 29, 2010 at 4:02 | comment | added | fedja | I can bring the cube to the class (I believe I still have it somewhere in my junk box). The question is then what exactly I should do with it, given that I do not want to spend the whole 75 minute class just talking about Rubik's cube but still want to demonstrate something non-trivial and funny. Any suggestions for, say, a 25 minute presentation? | |
| Jan 29, 2010 at 3:07 | history | answered | user1504 | CC BY-SA 2.5 |