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Something slightly interesting might be the Rubik's cube group. By considering the Rubik's cube a group under the rotation operation, then we can essentially co
by alderssc 16y ago
Something slightly interesting might be the Rubik's cube group. By considering the Rubik's cube a group under the rotation operation, then we can essentially completely solve the Rubik's cube puzzle.
If you are familiar with the Quaternions, take a look at the 3D rotation group SO(3). This group apparently has applications in computing where one needs a way to perform rotations in three dimensions. According to the Wikipedia article, https://secure.wikimedia.org/wikipedia/en/wiki/Quaternions_and_spatial_rotation https://secure.wikimedia.org/wikipedia/en/wiki/Quaternions_a..., this method of representation has certain important advantages over other methods, including being numerically stable and avoiding a problem called gimbal lock, where rotation about one of the possible axes is no longer possible.
- RiderOfGiraffes 16y agoWell, the idea of using commutators in the Rubik cube is what leads to a nice, elementary method of solving it, but it's not really a theorem or result from group theory that's telling us something we didn't already know. Plus I suspect many people would regard this as just a toy, a form of "play for play's sake" and hence still irrelevant. The fact that the quaternions form a field (hence two kinds of group, one of which is interesting) where the multiplication doesn't commute, and then that can be used to model rotations is again interesting, and can be asserted to be useful (and it is) but it's still not really what I'm looking for. But keep the ideas coming. There's got to be a good one out there somewhere - isn't there?