August 2007 - mathfun@mailman.xmission.com

Re: [math-fun] Matlab
by Eugene Salamin 22 Aug '07

22 Aug '07

----- Original Message ---- From: Bernie Cosell <bernie(a)fantasyfarm.com> To: math-fun <math-fun(a)mailman.xmission.com> Sent: Tuesday, August 21, 2007 6:41:37 AM Subject: [math-fun] Matlab We don't have any real need for it, but for a while now my wife and I have been kicking around the idea of getting a copy of Mathematica, mostly just for fun. I was poking around and discovered that "Matlab & Simulink" is *less*expensive* than Mathematica [$130 for the latter, $100 for the former]. Is Matlab "a good thing"? Will it do the sort of symbolic-computing and graphing that Mathematica will? /Bernie\ Maple has a student edition. It's $129 for Windows + Linux + Mac OS X. You will be asked for your educational institution and student ID number. I'm very pleased with Maple. A coworker who was a long time Mathematica user tried out Maple, and much preferred Maple. http://www.maplesoft.com/ But my real favorite is Macsyma, and I will go back to using it at work when it's resurrected. Ask RWG about how you might acquire a Macsyma. Gene ____________________________________________________________________________________ Shape Yahoo! in your own image. Join our Network Research Panel today! http://surveylink.yahoo.com/gmrs/yahoo_panel_invite.asp?a=7

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[math-fun] Matlab
by Bernie Cosell 21 Aug '07

21 Aug '07

We don't have any real need for it, but for a while now my wife and I have been kicking around the idea of getting a copy of Mathematica, mostly just for fun. I was poking around and discovered that "Matlab & Simulink" is *less*expensive* than Mathematica [$130 for the latter, $100 for the former]. Is Matlab "a good thing"? Will it do the sort of symbolic-computing and graphing that Mathematica will? /Bernie\ -- Bernie Cosell Fantasy Farm Fibers mailto:bernie@fantasyfarm.com Pearisburg, VA --> Too many people, too few sheep <--

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RE: [math-fun] Look and divide
by Eric Angelini 21 Aug '07

21 Aug '07

[Graeme and David]: > This means the sequence diverges ... yes, I'm afraid you're both right -- simplification or not, the seq diverges :-( Best and thanks, É. -----Message d'origine----- De : math-fun-bounces+eric.angelini=kntv.be(a)mailman.xmission.com [mailto:math-fun-bounces+eric.angelini=kntv.be@mailman.xmission.com] De la part de David Wilson Envoyé : mardi 21 août 2007 2:45 À : math-fun Objet : Re: [math-fun] Look and divide There are at least [10^(n-1)/n] fractions with numerator n, the smallest of which is at least [n/(10^(n-1))+n-1)]. This means that the fractions with numerator n add up to at least 10^(n-1)/(10^(n-1)+n-1), which approaches 1 for any n. This means the sequence diverges. ----- Original Message ----- From: "Eric Angelini" <Eric.Angelini(a)kntv.be> To: "math-fun" <math-fun(a)mailman.xmission.com> Sent: Monday, August 20, 2007 12:13 PM Subject: [math-fun] Look and divide Hello Math fun, read any fraction hereunder as: (quantity of digits used by the last term) ______________________________________________ (quantity of digits used in the sequence so far) Does the sum of all terms converge towards a precise number? (Sorry if this is old hat) Best, É. 0 1/1 2/3 2/5 2/7 2/9 2/11 3/14 3/17 3/20 3/23 3/26 3/29 ... (Example: the last fraction reads: "The preceding fraction uses 3 digits and the digits used so far in the sequence are 29") _______________________________________________ math-fun mailing list math-fun(a)mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun -- No virus found in this incoming message. Checked by AVG Free Edition. Version: 7.5.484 / Virus Database: 269.12.0/961 - Release Date: 8/19/2007 7:27 AM _______________________________________________ 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] Look and divide
by Eric Angelini 21 Aug '07

21 Aug '07

Hello Math fun, read any fraction hereunder as: (quantity of digits used by the last term) ______________________________________________ (quantity of digits used in the sequence so far) Does the sum of all terms converge towards a precise number? (Sorry if this is old hat) Best, É. 0 1/1 2/3 2/5 2/7 2/9 2/11 3/14 3/17 3/20 3/23 3/26 3/29 ... (Example: the last fraction reads: "The preceding fraction uses 3 digits and the digits used so far in the sequence are 29")

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[math-fun] fractal sequence
by Fred lunnon 19 Aug '07

19 Aug '07

This sequence arose in connection with divisibility of Stirling numbers of the first kind. It took me a while to figure out a (slightly clumsy) explicit expression for the n-th term. Seeing that things are a bit slack on the list just now, I thought I'd share it with everybody. The terms for n = 0, ..., 257 follow below --- should suffice for a wet afternoon! WFL [0, 0, 0, 1, 0, 3, 1, 2, 0, 5, 2, 4, 1, 5, 2, 3, 0, 7, 3, 6, 2, 7, 3, 5, 1, 7, 3, 6, 2, 7, 3, 4, 0, 9, 4, 8, 3, 9, 4, 7, 2, 9, 4, 8, 3, 9, 4, 6, 1, 9, 4, 8, 3, 9, 4, 7, 2, 9, 4, 8, 3, 9, 4, 5, 0, 11, 5, 10, 4, 11, 5, 9, 3, 11, 5, 10, 4, 11, 5, 8, 2, 11, 5, 10, 4, 11, 5, 9, 3, 11, 5, 10, 4, 11, 5, 7, 1, 11, 5, 10, 4, 11, 5, 9, 3, 11, 5, 10, 4, 11, 5, 8, 2, 11, 5, 10, 4, 11, 5, 9, 3, 11, 5, 10, 4, 11, 5, 6, 0, 13, 6, 12, 5, 13, 6, 11, 4, 13, 6, 12, 5, 13, 6, 10, 3, 13, 6, 12, 5, 13, 6, 11, 4, 13, 6, 12, 5, 13, 6, 9, 2, 13, 6, 12, 5, 13, 6, 11, 4, 13, 6, 12, 5, 13, 6, 10, 3, 13, 6, 12, 5, 13, 6, 11, 4, 13, 6, 12, 5, 13, 6, 8, 1, 13, 6, 12, 5, 13, 6, 11, 4, 13, 6, 12, 5, 13, 6, 10, 3, 13, 6, 12, 5, 13, 6, 11, 4, 13, 6, 12, 5, 13, 6, 9, 2, 13, 6, 12, 5, 13, 6, 11, 4, 13, 6, 12, 5, 13, 6, 10, 3, 13, 6, 12, 5, 13, 6, 11, 4, 13, 6, 12, 5, 13, 6, 7, 0, ...]

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RE: [math-fun] Golomb rulers
by Eric Angelini 17 Aug '07

17 Aug '07

Ok, crystal clear explanations, thanks a lot, David ! I'll check tonight the three seq and send them tomorrow to the OEIS if ok ! Best, É. -----Message d'origine----- De : math-fun-bounces+eric.angelini=kntv.be(a)mailman.xmission.com [mailto:math-fun-bounces+eric.angelini=kntv.be@mailman.xmission.com] De la part de David Wilson Envoyé : vendredi 17 août 2007 13:47 À : math-fun Objet : Re: [math-fun] Golomb rulers An n-mark Golomb ruler has a unique integer distance between any pair of marks, and thus measures n(n-1)/2 distinct integer distances. An optimal n-mark Golomb rulers has the smallest possible length (distance between the two end marks) for an n-mark ruler. A perfect n-mark Golomb ruler has length exactly n(n-1)/2, and measures each distance from 1 to n(n-1)/2. ----- Original Message ----- From: "Eric Angelini" <Eric.Angelini(a)kntv.be> To: "math-fun" <math-fun(a)mailman.xmission.com> Sent: Friday, August 17, 2007 6:31 AM Subject: [math-fun] Golomb rulers Hello, ... I am confused, having just read this on Eric Weisstein site: "However, the unique optimal Golomb 4-mark ruler is (0, 1, 4, 6), which measures the distances (1, 2, 3, 4, 5, 6) (and is therefore also a perfect ruler). As a further example, it turns out that the length of an optimal 6-mark Golomb ruler is 17. In fact, there are a total of four distinct 6-mark Golomb rulers, all of length 17, one of which is given by (0, 1, 4, 10, 12, 17). " http://mathworld.wolfram.com/GolombRuler.html ... What is the difference between a "perfect ruler" and an "optimal ruler" ?! ... I cannot measure 14 or 15 with (0, 1, 4, 10, 12, 17) Best, É. _______________________________________________ math-fun mailing list math-fun(a)mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun -- No virus found in this incoming message. Checked by AVG Free Edition. Version: 7.5.484 / Virus Database: 269.11.19/956 - Release Date: 8/16/2007 9:48 AM _______________________________________________ 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] Golomb rulers
by Eric Angelini 17 Aug '07

17 Aug '07

Hello, ... I am confused, having just read this on Eric Weisstein site: "However, the unique optimal Golomb 4-mark ruler is (0, 1, 4, 6), which measures the distances (1, 2, 3, 4, 5, 6) (and is therefore also a perfect ruler). As a further example, it turns out that the length of an optimal 6-mark Golomb ruler is 17. In fact, there are a total of four distinct 6-mark Golomb rulers, all of length 17, one of which is given by (0, 1, 4, 10, 12, 17). " http://mathworld.wolfram.com/GolombRuler.html ... What is the difference between a "perfect ruler" and an "optimal ruler" ?! ... I cannot measure 14 or 15 with (0, 1, 4, 10, 12, 17) Best, É.

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[math-fun] interesting-looking new book
by Thane Plambeck 16 Aug '07

16 Aug '07

http://press.princeton.edu/titles/8479.html blurb: "A Certain Ambiguity is an amazing narrative that glows with a vivid sense of the beauty and wonder of mathematics. The narrator is deeply troubled by the ancient question of whether the objects and theorems of mathematics have a reality independent of human minds. Mixing fiction with nonfiction, A Certain Ambiguity is a veritable history of mathematics disguised as a novel. Starting with the Pythagorean theorem, it moves through number theory and geometry to Cantor's alephs, non-Euclidean geometry, Gödel, and even relativity."--Martin Gardner -- Thane Plambeck tplambeck(a)gmail.com http://www.plambeck.org/ehome.htm

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[math-fun] Weak Skolem-Langford integers
by Eric Angelini 16 Aug '07

16 Aug '07

Hello Math-Fun & SeqFans, Could someone please compute for me all "weak Skolem-Langford" integers ? The sequence is finite (and ends, I guess, with 978416154798652002). http://www.research.att.com/~njas/sequences/A108116 Please find hereunder what I have found for integers of length 4, 6 and 8. Length 4: 2002 Length 6: 131003, 231213, 300131, 312132,420024 Length 8: 12132003, 14130043, 15120025, 23121300, 23421314, 25121005, 25320035, 30023121, 31213200, 31413004, 34003141, 40031413, 41312432, 45001415, 45121425, 45300435, 50012152, 51410054, 52002151, 52412154, 53002352, 53400354, 61310036, 62312136, 63001316, 63121326, 64200246. Lengths 10 to 18? Best, Éric A.

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Re: [math-fun] Tech question
by Dan Asimov 15 Aug '07

15 Aug '07

David writes: << Can someone give me the a few terms of the power series of the inverse of exp(x)-x at 0? Exact coefficients would be preferred if rational. >> The function f(x) := exp(x) - x has f'(0) = 0, so finv := f^(-1) does not possess a power series around 0 in the usual sense. There may be some ambiguity in the question. f(0) = 1, so is the desired series for the inverse function where its argument = 1 ??? Otoh, f(z) = 0 has a set of countably many solutions, symmetric about the x-axis, but with none of them *on* the axis. At any of these fixed points of exp(z), the derivative is nonzero and so the inverse function exists locally. Just as exp(z) has multiple branches of its inverse function, it's likely that exp(z) - z does the same. --Dan

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