November 2005 - mathfun@mailman.xmission.com

[math-fun] Need help for some tests
by Christian Boyer 17 Nov '05

17 Nov '05

I have new multiplicative magic squares of orders 10, 11, 12, 13, 14. I think that they are correct... but because stupid errors are always possible when objects use more than 100 integers, I search an external checking of the 5 examples. Who could check that the squares are correct? Use of distinct integers, good products, checking of broken diagonals for pandiagonal squares. Warning: magic products reaching 10^29. Any help will be appreciated! Send me a direct message, I will send you an Excel file (or a text file if you prefer) with the 5 squares ready to be checked. Thanks! Christian.

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Re: [math-fun] Need help for some tests
by Sterten＠aol.com 17 Nov '05

17 Nov '05

hi Christian, I think, I could do that. I need a text-file, (preferrably 1 number per line) Guenter. ------------------------------------- In einer eMail vom 16.11.2005 19:41:32 Westeuropäische Normalzeit schreibt cboyer(a)club-internet.fr: I have new multiplicative magic squares of orders 10, 11, 12, 13, 14. I think that they are correct... but because stupid errors are always possible when objects use more than 100 integers, I search an external checking of the 5 examples. Who could check that the squares are correct? Use of distinct integers, good products, checking of broken diagonals for pandiagonal squares. Warning: magic products reaching 10^29. Any help will be appreciated! Send me a direct message, I will send you an Excel file (or a text file if you prefer) with the 5 squares ready to be checked. Thanks! Christian. _______________________________________________ math-fun mailing list math-fun(a)mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun

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[math-fun] Re: Spiral of Fermat?
by Dean Hickerson 17 Nov '05

17 Nov '05

Gareth McCaughan wrote: > I'd guess (cynic that I am) that they're just utterly, utterly > confused, and are referring to FLT and getting both the dates > and the problem wrong. Unfortunately, that sounds very plausible. Dean Hickerson dean(a)math.ucdavis.edu

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[math-fun] maple? mathematica? or matlab OR magma ??
by MCKAY john 16 Nov '05

16 Nov '05

I am surprised not to have heard mention of magma. In my view this system from Sydney Australia, is the system of choice (ignoring cost) for deeper math. As for the original query: maple or mathematica, I use maple for algebra and GAp for groups (maple is grim here). But in my view maple development should stop. They are getting into thicker mire at each new version. -- I do not buy using ordinary numerical approximation where an exact mathod is called for. This makes some of PARI contentious. It is not mathematics to give probablistic answers without clear warnings! perhaps someone can tell us when numerical approximations are useful? I am used to converting to exact algebraic by using some LLL-type (PSLQ) algorithm - but other cases? John -- But leave the wise to wrangle, and with me the quarrel of the universe let be; and, in some corner of the hubbub couched, make game of that which makes as much of thee.

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RE: [math-fun] periodic (-1,0,1) matrices
by dasimov＠earthlink.net 16 Nov '05

16 Nov '05

Wouter wrote: << of the pseudo-anti-symmetric type (sum of anti-symmetric and diagonal). . . . . . . Funny property: only the even n give some matrices with all-zero diagonals, the odd n don't. >> Here's a proof that the odd n can't: Let M' := transpose of M. If M is an n-dim anti-symmetric (i.e., skew-symmetric) matrix for odd n, then det(M) = det(M') = det(-M) = (-1)^n det(M) = -det(M), so det(M) = 0, and so M can't be periodic. --Dan

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[math-fun] ??? maple, mathematica, matlab ???
by dasimov＠earthlink.net 16 Nov '05

16 Nov '05

I hope to buy one of {maple, mathematica, mathlab} to run on a Macintosh I'm planning to buy in the near future. I'd like to hear preferences and reasons from any of you who have used more than one of these. (I've never used matlab, but find that mathematica's incessant need for typing capital letters to begin each built-in command, together with its uniformly mediocre help files -- at least compared with maple's -- cause me to lean toward maple over mathematica. But I'd love to hear others' opinions. I'm curious about breadth of features, ease of use, and quality of graphics. (Price is relevant, too.) --Dan

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Fw: [math-fun] periodic (-1,0,1) matrices
by wouter meeussen 16 Nov '05

16 Nov '05

1. yes 2. yes 3. x x x 0 0 0 x x x 0 0 0 x x x 0 0 0 0 0 0 y y y 0 0 0 y y y 0 0 0 y y y is a 6-by-6 matrix, but just a couple of 3-by-3 matrices x-bloxk and y-block. Not surpising that they multiply independently. So, any multiplication or power property of the smaller blocks is 'cheap' : can be constructed from lower orders (order " in this case). For n=4, 96 matrices have period 12. For n=5, it's 2880. For n=6: 10728. W. -------------------------------------------- dasimov(a)earthlink.net wrote: Just to be sure I understand: 1. Are you referring to n x n matrices M = (m_ij) with all entries in {-1,0,1} such that i <> j => m_ij + m_ji = 0 ? 2. Do your divisors of 12 (for n = 6) include 12 itself? 3. What exactly is meant by "block matrices along the diagonal" ? Thanks for clarification, Dan

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RE: [math-fun] periodic (-1,0,1) matrices
by dasimov＠earthlink.net 15 Nov '05

15 Nov '05

Just to be sure I understand: 1. Are you referring to n x n matrices M = (m_ij) with all entries in {-1,0,1} such that i <> j => m_ij + m_ji = 0 ? 2. Do your divisors of 12 (for n = 6) include 12 itself? 3. What exactly is meant by "block matrices along the diagonal" ? Thanks for clarification, Dan -------------------------------------------------------------------------------------- Wouter wrote: << of the pseudo-anti-symmetric type (sum of anti-symmetric and diagonal). A072148. (cfr Aug 2003). Just submitted result for n=6. The periods still are divisors of 12. Weird. Realised that block matrices along the diagonal are cheap and predictable. So I did a count without'm, and eliminated sign change, transposes and mirroring over the anti-diagonal too. Got 1, 3, 12, 107, 951, 10923... (under submission). Funny property: only the even n give some matrices with all-zero diagonals, the odd n don't. But why period k | 12 ? >>

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[math-fun] periodic (-1,0,1) matrices
by wouter meeussen 15 Nov '05

15 Nov '05

of the pseudo-anti-symmetric type (sum of anti-symmetric and diagonal). A072148. (cfr Aug 2003). Just submitted result for n=6. The periods still are divisors of 12. Weird. Realised that block matrices along the diagonal are cheap and predictable. So I did a count without'm, and eleminated sign change, transposes and mirroring over the anti-diagonal too. Got 1, 3, 12, 107, 951, 10923... (under submission). Funny property: only the even n give some matrices with all-zero diagonals, the odd n don't. But why period k | 12 ? Wouter.

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[math-fun] Spiral of Fermat?
by Dean Hickerson 15 Nov '05

15 Nov '05

I ran across an article in The Humboldt Beacon (a newspaper published in Fortuna, CA) about a botanical garden that's being created at College of the Redwoods. Part of the garden is a double spiral walkway, in the shape of the Spiral of Fermat. (From a google search, I see that its polar equation is r^2 = theta.) The article has this paragraph, which I don't understand: Fermat first discussed his spiral equation in 1636, but he did not take the time to write the proof to it. The proof was developed over a number of years and finally confirmed in 2003. Does anyone know what this is about? What is there that needs to be proved about the spiral? Dean Hickerson dean(a)math.ucdavis.edu

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