In the latest update of www.multimagie.com, a new smallest known magic square of powers. A 144x144 magic square of 7th powers, constructed by Toshihiro Shirakawa. Magic sum = 3141592653589793238462643383279502884197169399375105. Amazing, all the digits of its magic sum are exactly the 52 first digits of Pi! And a reminder. On smallest possible magic squares, there still remain ten enigmas for winning €6,900 (~$9,500) and ten bottles of champagne. Christian.
That is truly magic! On Fri, Dec 13, 2013 at 7:13 AM, Christian Boyer <cboyer@club-internet.fr> wrote:
In the latest update of www.multimagie.com, a new smallest known magic square of powers. A 144x144 magic square of 7th powers, constructed by Toshihiro Shirakawa. Magic sum = 3141592653589793238462643383279502884197169399375105. Amazing, all the digits of its magic sum are exactly the 52 first digits of Pi!
And a reminder. On smallest possible magic squares, there still remain ten enigmas for winning €6,900 (~$9,500) and ten bottles of champagne.
Christian.
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Wonderful! I added it as a comment to http://oeis.org/A000796 On Fri, Dec 13, 2013 at 11:45 AM, James Buddenhagen <jbuddenh@gmail.com>wrote:
That is truly magic!
On Fri, Dec 13, 2013 at 7:13 AM, Christian Boyer <cboyer@club-internet.fr> wrote:
In the latest update of www.multimagie.com, a new smallest known magic square of powers. A 144x144 magic square of 7th powers, constructed by Toshihiro Shirakawa. Magic sum = 3141592653589793238462643383279502884197169399375105. Amazing, all the digits of its magic sum are exactly the 52 first digits of Pi!
And a reminder. On smallest possible magic squares, there still remain ten enigmas for winning €6,900 (~$9,500) and ten bottles of champagne.
Christian.
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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-- Dear Friends, I have now retired from AT&T. New coordinates: Neil J. A. Sloane, President, OEIS Foundation 11 South Adelaide Avenue, Highland Park, NJ 08904, USA. Also Visiting Scientist, Math. Dept., Rutgers University, Piscataway, NJ. Phone: 732 828 6098; home page: http://NeilSloane.com Email: njasloane@gmail.com
On Fri, Dec 13, 2013 at 6:13 AM, Christian Boyer <cboyer@club-internet.fr> wrote:
In the latest update of www.multimagie.com, a new smallest known magic square of powers. A 144x144 magic square of 7th powers, constructed by Toshihiro Shirakawa. Magic sum = 3141592653589793238462643383279502884197169399375105. Amazing, all the digits of its magic sum are exactly the 52 first digits of Pi!
Was the magic square constructed with that sum as a constraint so that, e.g. one could just as easily use the first 52 digits of e or phi; or is there really some deep connection with pi? -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
Toshihiro's magic square was constructed with that sum as a constraint, and also 7th powers as a constraint. He used the factorization of the 52 first digits of Pi: T1*T2 = (3^2*5*823*820555369677891747293) * 103378358491417482147378271 T1 = 30389268116020720860996255 T2 = 103378358491417482147378271 It was a good point to have T1 and T2 roughly of the same size, for the use of "taxicab" methods: split T1 (and T2) as sums of twelve 7th powers in at least twelve different ways. For example one way of T1: T1 = 1^7 + 555^7 + 1345 ^7 + 1426^7 + 2064^7 + 2371^7 + 2487^7 + 2812^7 + 3156^7 + 3437^7 + 3642^7 + 3755^7 Other ways, and construction method, are given at www.multimagie.com Toshihiro Shirakawa remains the ONLY person who has found solutions among my 12 enigmas of 2010. He solved two of them, that's why today there remain 10 enigmas. And he seems well placed to solve (in 2014?) a third one, #4c: ...construct a 7x7 magic square of cubes... Christian. -----Message d'origine----- De : math-fun-bounces@mailman.xmission.com [mailto:math-fun-bounces@mailman.xmission.com] De la part de Mike Stay Envoyé : samedi 14 décembre 2013 04:58 À : math-fun Objet : Re: [math-fun] Magic Pi On Fri, Dec 13, 2013 at 6:13 AM, Christian Boyer <cboyer@club-internet.fr> wrote:
In the latest update of www.multimagie.com, a new smallest known magic square of powers. A 144x144 magic square of 7th powers, constructed by Toshihiro Shirakawa. Magic sum = 3141592653589793238462643383279502884197169399375105. Amazing, all the digits of its magic sum are exactly the 52 first digits of Pi!
Was the magic square constructed with that sum as a constraint so that, e.g. one could just as easily use the first 52 digits of e or phi; or is there really some deep connection with pi? -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
participants (4)
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Christian Boyer -
James Buddenhagen -
Mike Stay -
Neil Sloane