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[math-fun] Re: 20th may, Historical date!
by Richard Guy 11 May '05

11 May '05

A little over 30 years ago, almost all nations agreed (when else has this happened? -- over the postal system, perhaps -- not over copyright ?) on the (adoption and) use of the ``metric system''. I quote from the Metric Style Guide: For example, April 7, 1975, is expressed as 1975 04 07. Alternative ways of writing this numeric date are 1975-04-07 or 19750407. Times can be appended, using the 24-hour clock. R. On Wed, 11 May 2005, Alonso Del Arte wrote: > As much sense as DDMMYYYY makes (smallest unit to largerst unit), many > of us live where MMDDYYYY is more prevalent, or even MMDDYY, as well > as miles and gallons. So here 20 May 2005 is 5/20/2005, hardly special > from the point of view of symmetry. Alonso > > On 5/10/05, alexandre.wajnberg(a)skynet.be <alexandre.wajnberg(a)skynet.be> wrote: >> >> Hello dear Seqfans and friends, >> >> Nicolas Graner (member of the Oulipo litterary movement) has devised a ... >

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Re: [math-fun] Waterman Polyhedra
by Mike Stay 11 May '05

11 May '05

Cool! Looks very reminiscent of Meyer's rational coloring of the sphere. http://math.ucsd.edu/~dmeyer/research/publications/ksnull/abs.html ----- Original Message Follows ----- > The Waterman polyhedra are apparently the convex hulls of > the centers of spheres in the fruitstand packing that lie > within a fixed radius of a fixed point. For large > distances, they closely approximate spheres. The original > image is very large, and the lacework of polyhedron edges > is clearly visible at full size. I have reduced it to a > 1024x768 wallpaper, in which the polyhedral faces are not > distinguishable, the overall impression is of a spherical > fractal with with a network of great circles emphasized. > > http://astronomy.swin.edu.au/~pbourke/polyhedra/waterman/index.html > > > - David W. Wilson > > "Truth is just truth -- You can't have opinions about the > truth." > - Peter Schickele, from P.D.Q. Bach's oratorio "The > Seasonings" > > > _______________________________________________ > math-fun mailing list > math-fun(a)mailman.xmission.com > http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun -- Mike Stay staym(a)clear.net.nz http://www.cs.auckland.ac.nz/~msta039

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RE: [math-fun] Why Math Matters: Scissors, paper, stone
by Daniel Asimov 10 May '05

10 May '05

>From an article by Steve Tomkins posted by Henry: << Scrabble meanwhile is a matter of fierce international championships, though it hasn't attracted so much interest from computers. Top players agree that one of the keys is learning all those two-letter words that seem to exist solely for the sake of Scrabble - like "aa" (a kind of lava) and "xu" (a monetary unit in Vietnam). >> Nonsense! This is a little like saying that "top chess players agree that one of the keys to winning chess is learning the rules of castling." It's true, but it's a drop in the bucket. Every Scrabble player in a Scrabble club has long since memorized the approx. 95 two-letter words that are fair play in Scrabble. The top-ranked Scrabble players I've met have actually memorized *all* the words that are legal in Scrabble. (They have no idea what most of them mean, but hey.) --Dan

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[math-fun] Binet form
by David Wilson 10 May '05

10 May '05

Someone recently refered to Fib(n) = (sqrt(5)/5) ((1+sqrt(5))/2)^n - (1-sqrt(5))/2)^n) as the Binet form of the Fibonacci numbers. Would the term "Binet form" apply to any such explicit formula for a linear recurrence? - David W. Wilson "Truth is just truth -- You can't have opinions about the truth." - Peter Schickele, from P.D.Q. Bach's oratorio "The Seasonings"

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[math-fun] ham :-)
by David Wilson 10 May '05

10 May '05

I checked my Spambayes options, and I can indeed omit "ham" from the "To:" line of good mail while keeping "spam" in the "To:" line of spam. Presumably there will be no more problems with the "ham" recipient from my end. - David W. Wilson "Truth is just truth -- You can't have opinions about the truth." - Peter Schickele, from P.D.Q. Bach's oratorio "The Seasonings"

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[math-fun] ham
by David Wilson 10 May '05

10 May '05

You will notice that my posts sometimes often include "ham" among the recipients. This will result in a bounce if you "reply all" to my posts, and several people have commented on this. By way of explanation: I am currently using MicroSuck Outlook Express, the free but rather hobbled version of Outlook that came on my PC. About a year ago, my spam ratio finally exceeded my patience ratio. Since Outlook Express does not provide an effective spam filter, I decided to try Spambayes, of which I had heard good things (which were true). Most mail programs provide API hooks allowing Spambayes filtering to be integrated into the program. Not so Outlook Express. When using Spambayes with Outlook Express, Spambayes must be inserted upstream of Outlook Express, where it marks incoming mail so that Outlook Express can classify it using its (lame) native mail filters. From a small number of unsavory choices, Spambayes chose to include "ham", "spam" or "unsure" in the "To:" line, so that Outlook Express could identify and route spam by detecting "spam" in the "To:" line. I am guessing that this Spambayes feature was included solely to deal with Outlook Express. Unfortunately, because good incoming mail has "ham" in the "To:" line, "ham" is replicated to the "To:" line of reply-alls to that mail. If I fail to remove "ham" from the recipients, it makes its way into the mailing list and subsequent "reply-alls". Since "ham" is not a valid recipient, bounces occur. I don't know if Seqfan and Math-Fun could filter "ham" out of the "To:" line of incoming mail, this would solve the mailing list problem. A more general solution would be for Spambayes to allow me to put "spam" in the "To:" line of spam, but leave the "To:" line of ham alone; this is consistent with my own personal mail filtering. - David W. Wilson "Truth is just truth -- You can't have opinions about the truth." - Peter Schickele, from P.D.Q. Bach's oratorio "The Seasonings"

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[math-fun] Courtesy
by David Wilson 10 May '05

10 May '05

Just a reminder. As a courtesy to subscribers who labor under restrictions or charges for downloads or disk space, Seqfan and Math-Fun mailing lists encourage voluntarily limiting the size of messages. We should all try to avoid posting huge data tables, large amounts of irrelevant quoted text, and/or data file attachments where possible. Personally, if a have voluminous data that I think may be of interest to list, I will offer my data on request. ----- Original Message ----- From: "Robert G. Wilson v" <rgwv(a)rgwv.com> To: <ham>; <alexandre.wajnberg(a)skynet.be> Cc: "Eric Angelini" <keynews.tv(a)skynet.be>; <seqfan(a)ext.jussieu.fr> Sent: Monday, May 09, 2005 7:55 PM Subject: Re: Semiprime's dividers concatenated > Dear Alexandre, > > They do not quite cycle. Using the Mathematica coding: > t = Union[ Flatten[ Table[ FromDigits[ Join[ IntegerDigits[ Prime[i]], > IntegerDigits[ Prime[j]]]], {i, 250}, {j, 250}]]]; Mod[t, 10] produces a > sequence that never quite falls into a pattern. > > Sincerely yours, Bob. > > 2, 3, 5, 7, 2, 3, 5, 7, 2, 3, 5, 7, 2, 3, 5, 7, 2, 3, 5, 7, 2, 3, 5, 7, 2, > 3, 5, [Very large data table and remainder of message elided]

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[math-fun] polygon inscribing constant
by R. William Gosper 10 May '05

10 May '05

is Weisstein's name for the x = pi case of inf /===\ | | x | | cos(-), | | n n = 3 the inner/outer radius ratio of the annular nesting of all the regular polygons, alternated with circles. (With the right z(r), might make a nice drinking cup.) Perhaps equivalent to his Mathworld circumscribing formula, simply expand the log of the quadrisected product, inf inf inf /===\ /===\ /===\ | | x | | x | | x log(( | | cos(-------)) ( | | cos(-------)) ( | | cos(-------)) | | 4 n + 3 | | 4 n + 4 | | 4 n + 5 n = 0 n = 0 n = 0 inf /===\ | | x | | cos(-------)) | | 4 n + 6 n = 0 4 i 2 i 2 B pi inf 2 i 2 i i 2 i 2 i ==== (1 - 2 ) B (--------------- + (- 1) (2 + 1)) x \ 2 i 2 (2 i)! = > ---------------------------------------------------------- , / 2 i (2 i)! ==== i = 1 a series with convergence radius 3 pi/2, hence 2 lg 3 - 2 ~ 1.17 bits/term. Note the unusual Bern^2. Because B_n ~ n!/(2 pi)^n, the radius appears to be only pi/2 (useless), but the factor 4 i 2 i 2 B pi i 2 i 2 i i 2 i (- 1) 2 --------------- + (- 1) (2 + 1) ~ - ----------- 2 (2 i)! 2 i 3 saves the day, at the cost of 3.17 bits/term of subtractive cancellation. Adding more terms without raising the intermediate precision will actually ruin your accuracy. To 30 places, 1/8.70003662520819450322240985911. --rwg

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[math-fun] (Fwd) [NOBNET 4625] Mathematical Games
by Bernie Cosell 09 May '05

09 May '05

I know that in addition to your likely being interested in this, I know that several of you have contributed to Mathematical Games over the years and so might want to get in touch with Ed... /Bernie\ ------- Forwarded message follows ------- Date: Mon, 8 Nov 2004 06:30:37 -0800 (PST) From: ed pegg <ed(a)mathpuzzle.com> Subject: [NOBNET 4625] Mathematical Games To: nobnet(a)iijnet.or.jp Martin Gardner just recently celebrated his 90th birthday. Also, maa.org is *finally* releasing the entire collection of Mathematical Games on CD rom next month. There were frightening amounts of copyright issues to work out, but they have been resolved. Catalog Code: TDG/FW04 ISBN 0-88385-545-3 List Price: $54.95 This is all 15 Mathematical Games books on a CD-Rom. I'd like to do a "behind the scenes" look at Mathematical Games for an article. Martin did lots, but he avidly used a lot of help from hundreds of people. I'd like to write an article about the background help. If you ever assisted in one of Martin's columns, I'd like to hear from you -- a note about what you did. I'll use these notes in my article. Ed Pegg Jr http://www.maa.org columnist http://www.mathpuzzle.com ------- End of forwarded message ------- -- Bernie Cosell Fantasy Farm Fibers mailto:bernie@fantasyfarm.com Pearisburg, VA --> Too many people, too few sheep <--

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[math-fun] While playing with A103314
by David Wilson 08 May '05

08 May '05

In attacking A103314, I decided to try to plot the sums of subsets of the roots of 1. For square roots, I got 1 2 1 where numbers count multiplicities of points. The 2 at the origin corresponds to A103314(2) = 2. For cube roots, I got 1 1 1 2 1 1 1 so A103314(3) = 2. For fourth roots, I got 1 2 1 2 4 2 1 2 1 so that A103314(4) = 4. Now, notice that the square root plot includes the vertices you would see sighting a square along its diagonal. The cube root plot includes the vertices you would see sighting a cube along its great diagonal. Is the fourth root plot what you would (might) see sighting a tesseract along its great diagonal? Does the analogy extend to higher roots? - David W. Wilson "Truth is just truth -- You can't have opinions about the truth." - Peter Schickele, from P.D.Q. Bach's oratorio "The Seasonings"

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