October 2009 - mathfun@mailman.xmission.com

Re: [math-fun] The word "stathm"
by Dan Asimov 18 Oct '09

18 Oct '09

Allan wrote [of stathm]: << It's too cute a word to stay out of the dictionary. Yes, but . . . there are precious few citations for it. Googling on +stathm algebra only 10 distinct citations come up (ignoring the ones Google calls "similar"). Meanwhile, MathSciNet has *zero* occurrences of the word *anywhere* in their database (though there are maybe five for foreign versions of the word). (But besides not being in the OED, it's also not in either the 2nd or 3rd edition of Merriam-Webster's unabridged.) --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele

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[math-fun] Numbering Houses on Streets
by Hans Havermann 16 Oct '09

16 Oct '09

An article in today's Toronto Star outlines a program for residents in a nearby community "to remove unlucky digits from their addresses": http://www.thestar.com/news/gta/article/711189--may-the-4-s-be-with-you-not… The vagaries of house numbering is what makes map-applications' address-finding feature the more-or-less hit-or-miss proposition that only in-the-field intelligence (such as, if available, Google's street view) will ever really solve. I was surprised some years ago to find houses on one side of a street (outside of St. John's, Newfoundland) numbered sequentially! I had taken the even-odd dichotomy for granted.

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[math-fun] solution to the financial crisis
by rcs＠xmission.com 16 Oct '09

16 Oct '09

Cryptarithm: PRINT + MORE = MONEY. Task: Minimal & Maximal solutions; How Many? If you post an answer, include spoiler protection. Rich (PS for newcomers: This is a math puzzle, not an invitation to comment on the wisdom of our governments' actions.)

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[math-fun] Clumpy heapsort
by Steve Witham 14 Oct '09

14 Oct '09

Here is as far as I've gone with the clumpy heapsort layout: http://www.tiac.net/~sw/2009/10/Clumpy_heapsort The one-argument recursive definition of the sequence (starting at one instead of zero) is: def A082008( n ): if n == 1: return 1 y = 2 ** int( log( n, 2 ) ) yc = 2 ** 2 ** int( log( log( y, 2 ), 2 ) ) yr = y / yc return (yc-1) * int( (n-y) / yr + 1 ) + A082008( yr + n % yr ) --Steve

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Re: [math-fun] The word "stathm"
by Dan Asimov 13 Oct '09

13 Oct '09

HIlarie wrote: << "stathmic" is mentioned as a generic term for weight measure in http://www.anistor.gr/history/DIO_Support.html "homostathmy" and "heterostathmy" --- you know, when you measure the distance between anthers and stigma. "stathmin" is a microtubule-destabilizing protein >> Hmm, interesting. --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele

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[math-fun] The word "stathm"
by Dan Asimov 13 Oct '09

13 Oct '09

We were taught in Algebra that a stathm is a function on a ring that can be used like absolute value on the integers to prove the Euclidean algorithm. It's in some math books, but I can't find it in any dictionary, not even the OED. Does anyone know of any dictionary where this word appears? --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele

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Re: [math-fun] The word "stathm"
by Dan Asimov 13 Oct '09

13 Oct '09

RWG writes: << Anybody have an "in" at MW? (Which gives stathmokinesis and stathm=landing place.) . . . 'Taint math, but I like "stloppus">> Y'mean as in "We can do whatever we wlant; you can't stloppus" ? But seriously, there is an editor at MW I've been corresponding with for quite a while. I could try her. --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele

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Re: [math-fun] The word "stathm"
by Dan Asimov 13 Oct '09

13 Oct '09

Thanks for the responses! Allan writes: << What a cool word. There are a few Greek words with this stem, which all seem to share a sense of measuring, aligning, or marking out. The feminine noun "stathma" or "stathme" means a carpenter's rule or line; the masculine "stathmos" is an animal's rectangular stall. The verb "stathmao" means "measure by rule." The neuter noun "stathmon" means a weight. I'm not sure if all of these have the same etymological origin. >> Interesting. Wow, you know Greek?! --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele

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Re: [math-fun] Little math competition problem
by Gareth McCaughan 11 Oct '09

11 Oct '09

On Saturday 10 October 2009 23:36:18 Victor Miller wrote: [me:] >>> [mod-2 stuff] [Richard Guy:] >> (x + 3/2)^2 + (y + 3/2)^2 + (z + 3/2)^2 = -7/4. R. [Victor:] > Except that -7/4 -3*9/4=-34/4. You want the + sign. Oh yeah. (And indeed it turns out that x=[sqrt(7)-3]/2, y=z=-3/2, solves the original equation. Just not rationally.) So maybe I'm not an idiot after all. -- g

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Re: [math-fun] Little math competition problem
by Gareth McCaughan 10 Oct '09

10 Oct '09

On Thursday 08 October 2009 21:10:02 Dan Asimov wrote: > Find all rational solutions of > > x^2 + y^2 + z^2 + 3(x + y + z) + 5 = 0. Since no one else has bitten yet, here's a solution after some spoiler space. THIS SPACE INTENTIONALLY LEFT BLANK THIS SPACE INTENTIONALLY LEFT BLANK THIS SPACE INTENTIONALLY LEFT BLANK THIS SPACE INTENTIONALLY LEFT BLANK THIS SPACE INTENTIONALLY LEFT BLANK THIS SPACE INTENTIONALLY LEFT BLANK THIS SPACE INTENTIONALLY LEFT BLANK THIS SPACE INTENTIONALLY LEFT BLANK THIS SPACE INTENTIONALLY LEFT BLANK THIS SPACE INTENTIONALLY LEFT BLANK THIS SPACE INTENTIONALLY LEFT BLANK THIS SPACE INTENTIONALLY LEFT BLANK THIS SPACE INTENTIONALLY LEFT BLANK THIS SPACE INTENTIONALLY LEFT BLANK THIS SPACE INTENTIONALLY LEFT BLANK THIS SPACE INTENTIONALLY LEFT BLANK THIS SPACE INTENTIONALLY LEFT BLANK THIS SPACE INTENTIONALLY LEFT BLANK THIS SPACE INTENTIONALLY LEFT BLANK THIS SPACE INTENTIONALLY LEFT BLANK THIS SPACE INTENTIONALLY LEFT BLANK There are no rational solutions. Let x=a/n etc. with minimal n. Then we're solving x^2 + y^2 + z^2 + 3n(x+y+z) + 5n^2 = 0; not all of x,y,z,n are even. If 4|n then 4|x^2+y^2+z^2, whence x,y,z are all even, contradiction. If n is odd then x^2+3nx etc. are all even, so the LHS is odd, hence nonzero; contradiction. So n=2m, m odd. Complete the squares, writing u=x+3m etc.; we get u^2+v^2+w^2 = 7m^2 but the RHS is 7 (mod 8) which the LHS cannot be. (We could replace the last three paragraphs with "Now just try all possibilities for x,y,z,n mod 4 and observe that none of them works.") -- g

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