Comments on: Geomagic squares http://cameroncounts.wordpress.com/2011/01/21/geomagic-squares/ always busy counting, doubting every figured guess . . . Wed, 19 Jun 2013 18:15:17 +0000 hourly 1 http://wordpress.com/ By: Peter Cameron http://cameroncounts.wordpress.com/2011/01/21/geomagic-squares/#comment-1985 Mon, 07 Feb 2011 16:05:53 +0000 http://cameroncounts.wordpress.com/?p=1020#comment-1985 Good question. I don’t think there is a very close connection, since the group of transformations of the Rubik cube is definitely not embeddable into the Euclidean group. However, we could imagine a reformulation, where the 26 small cubes making up the Rubik cube had little bumps and hollows to ensure that they could only fit together in the way which actually solved the cube; you are allowed to move them around but cannot build the cube without actually solving it. Trouble is, I am not quite sure that you can build the constraints of the actual moves in this model.

]]> By: Peter Cameron http://cameroncounts.wordpress.com/2011/01/21/geomagic-squares/#comment-1984 Mon, 07 Feb 2011 16:02:48 +0000 http://cameroncounts.wordpress.com/?p=1020#comment-1984 In the 19th century, Felix Klein proposed the viewpoint that geometry is the study of properties invariant under prescribed transformation groups. This would mean that potentially anything could be counted as geometry. But I don’t think this is what you mean.

If geometry is 2- and 3-dimensional Euclidean geometry, then surely the answer is no. For several reasons: first, I could take some set-up whose symmetries were not contained in the Euclidean group; second, I could imagine problems about infinite sets larger than the cardinality of Euclidean space.

]]> By: Wesley Parish http://cameroncounts.wordpress.com/2011/01/21/geomagic-squares/#comment-1920 Thu, 27 Jan 2011 08:23:44 +0000 http://cameroncounts.wordpress.com/?p=1020#comment-1920 Any thoughts on the application of this to the (in)famous Rubics Cube?

]]> By: Alex Leibowitz http://cameroncounts.wordpress.com/2011/01/21/geomagic-squares/#comment-1919 Thu, 27 Jan 2011 01:16:58 +0000 http://cameroncounts.wordpress.com/?p=1020#comment-1919 Because to my mind, geometry is always clearer than set theory.

]]> By: Alex Leibowitz http://cameroncounts.wordpress.com/2011/01/21/geomagic-squares/#comment-1918 Thu, 27 Jan 2011 01:16:16 +0000 http://cameroncounts.wordpress.com/?p=1020#comment-1918 If one can treat geometrical problems set theoretically, is it possible to treat set theoretical problems geometrically?

]]> By: Peter Cameron http://cameroncounts.wordpress.com/2011/01/21/geomagic-squares/#comment-1917 Wed, 26 Jan 2011 14:55:50 +0000 http://cameroncounts.wordpress.com/?p=1020#comment-1917 The New Scientist article is here.

]]> By: Android OS news » Ancient Puzzle Gets New Lease on ‘Geomagical’ Life http://cameroncounts.wordpress.com/2011/01/21/geomagic-squares/#comment-1914 Wed, 26 Jan 2011 11:08:17 +0000 http://cameroncounts.wordpress.com/?p=1020#comment-1914 [...] information and in the design of drug trials so geomagic ones may have real-world uses, says mathematician Peter Cameron. New Scientist has also put up a gallery of the geomagic [...]

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