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Re: [OT] Re: Rubik Cube

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.

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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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Thread

[OT] Re: Rubik Cube "Mr. Man-wai Chang" <toylet.toylet@gmail.com> - 2016-12-06 13:02 +0800
  Re: [OT] Re: Rubik Cube edrhodes@hotmail.com - 2016-12-06 06:24 -0800
    Re: [OT] Re: Rubik Cube "Mr. Man-wai Chang" <toylet.toylet@gmail.com> - 2016-12-06 23:04 +0800
      Re: [OT] Re: Rubik Cube edrhodes@hotmail.com - 2016-12-06 07:23 -0800
      Re: [OT] Re: Rubik Cube joeturn <joeturn2@yahoo.com> - 2016-12-06 10:24 -0800
        Re: [OT] Re: Rubik Cube joeturn <joeturn2@yahoo.com> - 2016-12-06 10:29 -0800
          Re: [OT] Re: Rubik Cube joeturn <joeturn2@yahoo.com> - 2016-12-06 10:41 -0800
            Re: [OT] Re: Rubik Cube joeturn <joeturn2@yahoo.com> - 2016-12-06 10:54 -0800
        Re: [OT] Re: Rubik Cube "Mr. Man-wai Chang" <toylet.toylet@gmail.com> - 2016-12-07 11:26 +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 10:38 +0800
        Re: [OT] Re: Rubik Cube marston shores <kp@of.fire> - 2016-12-07 09:47 -0700
      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
    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 20:33 +0800
        Re: [OT] Re: Rubik Cube "K Wills (Shill #3)" <compuelf@gmail.com> - 2016-12-07 18:25 -0600
      Re: [OT] Re: Rubik Cube marston shores <kp@of.fire> - 2016-12-07 09:48 -0700

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