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RE: [math-fun] Huge fraction
by Eric Angelini 22 Aug '07

22 Aug '07

Ok, I have it, sorry : Sum of first 1000 terms = 8.8065157488607 Sum of first 10000 terms = 11.3162897519777 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 Eric Angelini Envoyé : mercredi 22 août 2007 18:04 À : math-fun Objet : [math-fun] Huge fraction Hello Math-Fun, I'm sorry to bother with this, but could someone compute this fraction? The result should be close to 4, I guess. (This is the sum of the first 10000 fractions of my previous "look and divide" diverging seq. The fractions are simplified immediately before computing the next term; thus the first "1" was "1/1" before simplification and the second "1/2" was "2/4"). Best, É. (there are 193 "return carriage" marks on my page and the fraction bar "/" is in yellow) http://www.cetteadressecomportecinquantesignes.com/Fraction.htm 0 1 1/2 1/2 1/3 1/4 1/5 1/6 1/7 1/8 1/9 1/10 3/23 3/26 3/29 3/32 3/35 3/38 3/41 3/44 3/47 3/50 3/53 3/56 3/59 3/62 3/65 3/68 3/71 3/74 3/77 3/80 3/83 3/86 3/89 3/92 3/95 3/98 3/101 4/105 ... etc. _______________________________________________ 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] Huge fraction
by Eric Angelini 22 Aug '07

22 Aug '07

Hello Math-Fun, I'm sorry to bother with this, but could someone compute this fraction? The result should be close to 4, I guess. (This is the sum of the first 10000 fractions of my previous "look and divide" diverging seq. The fractions are simplified immediately before computing the next term; thus the first "1" was "1/1" before simplification and the second "1/2" was "2/4"). Best, É. (there are 193 "return carriage" marks on my page and the fraction bar "/" is in yellow) http://www.cetteadressecomportecinquantesignes.com/Fraction.htm 0 1 1/2 1/2 1/3 1/4 1/5 1/6 1/7 1/8 1/9 1/10 3/23 3/26 3/29 3/32 3/35 3/38 3/41 3/44 3/47 3/50 3/53 3/56 3/59 3/62 3/65 3/68 3/71 3/74 3/77 3/80 3/83 3/86 3/89 3/92 3/95 3/98 3/101 4/105 ... etc.

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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 20 Aug '07

20 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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