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Groups > comp.programming > #7089
| From | David Brown <david.brown@hesbynett.no> |
|---|---|
| Newsgroups | alt.conspiracy, comp.programming, alt.mythology |
| Subject | Re: [OT] Re: Rubik Cube |
| Date | 2016-12-08 10:58 +0100 |
| Organization | A noiseless patient Spider |
| Message-ID | <o2bap7$hcd$1@dont-email.me> (permalink) |
| References | <o25gc3$jsk$1@news.mixmin.net> <o25gnf$bh8$2@dont-email.me> <87ede84c-c196-4e44-956f-7e1729be4963@googlegroups.com> <o26k08$ogb$3@dont-email.me> |
Cross-posted to 3 groups.
On 06/12/16 16:04, Mr. Man-wai Chang wrote: > On 6/12/2016 10:24 PM, edrhodes@hotmail.com wrote: >>>> >>>> Rubik Cube <https://s16.postimg.org/5r2hg8z4l/Rubik_Cube.png> >>>> Rubik Cube <http://i.imgur.com/aLzn76G.png> >>> >>> Only evils and daemons know how to play with and solve it? :) >> >> Got stumped, huh? >> > > Is there really continuous mathematics in solving Rubik Cube? In mathematics, "continuous" has a particular meaning - it means there are no individual steps (or the steps can be made as small as you like). If you balance a Rubik's Cube on the end of your finger and spin it, the movement is continuous. But if you move the layers on the cube, the movement is discrete. You can turn a face once, twice, three times, etc., but not half a turn (at least not if you want to get very far). Thus the mathematics of the Rubik's Cube is discrete, not continuous. > Matrix? A matrix is a way of organising numbers or other mathematical entities in a two-dimensional array. I can't think off-hand how they would be particularly useful in describing the maths of a Rubik's Cube. > > But is matrix mathematics at all? Yes, matrices are extremely useful in many fields of mathematics. > Or just some sine-cosine-tangent > tables that needs to be memorized? No, trigonometry is not useful for Rubik's Cubes (except when drawing 3D images of them). The key mathematics of Rubik's Cubes is group theory. The positions on the cube form a rather large and complicated group with a lot of interesting cyclic patterns. For mathematicians who like algebra and group theory, it is a lovely real-world example of such groups. But for most people, the group theory has no relevance to /solving/ the cube. It is only "mathematical" in that people usually solve it using logical methods and a clear structured algorithm. Typically this is done by memorizing sequences with specific effects (like swapping two cubes while leaving the others unchanged), and applying these sequences in an appropriate order. If you are interested in the maths, you can take a solved cube and pick a short sequence of moves. Repeat this sequence, and count how many repetitions are needed to return the cube to solved. It will /always/ get back to the starting point, no matter what sequence you use. It can be interesting to look at the prime factors of the sequence length, and see how the same factors turn up regularly - they will all be factors of the number of positions in the cube (43,252,003,274,489,856,000).
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Re: [OT] Re: Rubik Cube "Mr. Man-wai Chang" <toylet.toylet@gmail.com> - 2016-12-06 23:04 +0800
Re: [OT] Re: Rubik Cube "K Wills (Shill #3)" <compuelf@gmail.com> - 2016-12-07 03:47 -0600
Re: [OT] Re: Rubik Cube "Mr. Man-wai Chang" <toylet.toylet@gmail.com> - 2016-12-07 20:32 +0800
Re: [OT] Re: Rubik Cube "K Wills (Shill #3)" <compuelf@gmail.com> - 2016-12-07 18:24 -0600
Re: [OT] Re: Rubik Cube Kaz Kylheku <221-501-9011@kylheku.com> - 2016-12-08 01:36 +0000
Re: [OT] Re: Rubik Cube "Mr. Man-wai Chang" <toylet.toylet@gmail.com> - 2016-12-08 10:36 +0800
Re: [OT] Re: Rubik Cube Ben Bacarisse <ben.usenet@bsb.me.uk> - 2016-12-08 02:56 +0000
Re: [OT] Posting algorithm "Mr. Man-wai Chang" <toylet.toylet@gmail.com> - 2016-12-08 12:31 +0800
Re: [OT] Re: Rubik Cube "Mr. Man-wai Chang" <toylet.toylet@gmail.com> - 2016-12-08 10:37 +0800
Re: [OT] Re: Rubik Cube marston shores <kp@of.fire> - 2016-12-07 09:47 -0700
Re: [OT] Re: Rubik Cube fir <profesor.fir@gmail.com> - 2016-12-07 07:01 -0800
Re: [OT] A: Rubik Cube equation? "Mr. Man-wai Chang" <toylet.toylet@gmail.com> - 2016-12-08 10:45 +0800
Re: [OT] Re: Rubik Cube David Brown <david.brown@hesbynett.no> - 2016-12-08 10:58 +0100
Re: [OT] Re: Understanding mathematics through learning "Mr. Man-wai Chang" <toylet.toylet@gmail.com> - 2016-12-08 21:30 +0800
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