October 2007 - mathfun@mailman.xmission.com

Re: [math-fun] 3-D spider webs?
by James Propp 07 Oct '07

07 Oct '07

Dan Asimov writes: >Just Friday I turned over an 8-inch rock from our garden0, >and clinging to the bottom were two thin earthworms and >a paperish thing that resembled the remains of some kind >of cocoon. When that thing started flexing, I thought we >were about to witness the emergence of some insect's next >stage. But instead -- after about five minutes of flexing -- >out walked a spider -- a black one quite fat (probably expecting) -- >looking quite formidable. > >I don't know if this was a "web" or not, but maybe not, given >it was under a rock. Probably the spider was planning to go to >sleep and wake up as one or more newborn spiders. Cool. Thanks, Dan! Jim

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Re: [math-fun] 3-D spider webs?
by Dan Asimov 07 Oct '07

07 Oct '07

Jim asks: << Do any spiders build genuinely three-dimensional webs? Just Friday I turned over an 8-inch rock from our garden0, and clinging to the bottom were two thin earthworms and a paperish thing that resembled the remains of some kind of cocoon. When that thing started flexing, I thought we were about to witness the emergence of some insect's next stage. But instead -- after about five minutes of flexing -- out walked a spider -- a black one quite fat (probably expecting) -- looking quite formidable. I don't know if this was a "web" or not, but maybe not, given it was under a rock. Probably the spider was planning to go to sleep and wake up as one or more newborn spiders. --Dan

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Re: [math-fun] nuclear pennies
by James Propp 07 Oct '07

07 Oct '07

Apropos of nuclear pennies (which I'll call the "1+x^2 <--> x" game, for reasons that will be clear to anyone who read the "A Neighborhood of Infinity" web-page on the topic), here are some similar games: 1) The "2x --> 1+x^2" game. This is also called chip-firing, and a lot is known about it, although a lot is still mysterious: see the article "Disks, Balls, and Walls: Analysis of a Combinatorial Game" by Anderson, Lovasz, Shor, Spencer, Tardos, and Winograd (American Mathematical Monthly 96 (1989), 481-493; available on JSTOR and probably elsewhere as well). (I don't know whether anyone has explored the 1+x^2 --> 2x game. If you start with 2n+1 pennies in a row and start consolidating them via this rule, what are the terminal configurations that can result?) 2) The "x <-> 2" game. This is a sort of variant of chip-firing that can be used to construct the real numbers via their binary representations; see the article "The real numbers as a wreath product" by Faltin, Metropolis, Ross, and Rota; Advances in Math. 16 (1975), 278-304). It's somewhat amazing to me that the construction of the reals via radix expansion isn't better known. Everyone thinks it must be incredibly ugly, but with the right approach it's no more complicated than cuts or Cauchy sequences. 3) The "3x <--> x^2+2" game. This is related to what I call the "unary-binary system" of representing positive integers, via strings of digits like 10.2 that means the same thing whether you interpret them as extended unary or extended binary (1x^1 + 0x^0 + 2x^(-1) is three regardless of whether x is 1 or 2). Jim Propp

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[math-fun] 3-D spider webs?
by James Propp 07 Oct '07

07 Oct '07

Olivier Gerard wrote: >Hello, > >I just spotted an old article of National Geographic > >http://news.nationalgeographic.com/news/2004/06/0624_040624_tvspider.html [etc.] The movie "The Last Mimzy" featured a boy who, under the influence of various pedagogical artifacts from the future, creates a prize-winning science fair project by inducing spiders to build three-dimensional webs. Do any spiders build genuinely three-dimensional webs? (I am not counting random amorphous webs like the ones described in http://www.nytimes.com/2007/08/31/us/31spider.html?_r=1&oref=slogin but webs whose three-dimensionality is architectural.) Jim Propp

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Re: [math-fun] Arnold.rtf (was SJMathCircle (Was nuclear pennies))
by Hilarie Orman 07 Oct '07

07 Oct '07

http://hilarie.orman.name:8013/other/gosper-arnold.gif

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[math-fun] Arnold.rtf (was SJMathCircle (Was nuclear pennies))
by Steve Witham 06 Oct '07

06 Oct '07

>From: Bill Gosper <rwmgosper(a)yahoo.com> > > Would they be willing >guinea pigs for my latest disk puzzle? (http://gosper.org/Arnold.rtf .) You might think that rtf was a standard format, but apparently, you can include pictures in there that not all rtf, er, renderers can render. Rtf is interesting because inside it's all text, and Arnold.rtf begins... {\rtf1\ansi\ansicpg1252\deff0\deflang1033 {\fonttbl{\f0\fswiss\fcharset0 Arial;}} {\*\generator Msftedit 5.41.15.1507;} i.e. Created by Microsoft Edit \viewkind4\uc1\pard\qc\f0\fs36 Arnold Dozenegger \par \par \fs20{\object\objemb{\*\objclass Paint.Picture} I don't know if that's from the Paint program in Windows or just a format they use. Maybe if you made it a .bmp or .gif, more programs could display it. Don't know how to do that in your context. \objw8310\objh7800{\*\objdata 01050000 02000000 ... and megabytes and megabytes of hex digits. On my Mac, I can't see the picture with these: TextEdit (the Mac's default rtf editor) AppleWorks (the former Word substitute) but I can with NeoOffice (OpenOffice with a Mac (non-X) front end) I don't have Apple's "Pages" to try. By the way, zipping the file reduces it from 8.6MB to 220KB-- "39 times as small!" If you tell zip (winzip, pkzip) to use its oldest format, Macs have a better chance of decoding it. --Steve p.s. it's strange how a megabyte is large for email and tiny for disk space. A typical novel is about a megabyte. We are at the point where it's like mailing a book vs. keeping a book in a large library. (& a flash card or USB drive is like carrying a small library around in your pocket.)

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[math-fun] twelve disks inside an oval
by Alan Schoen 06 Oct '07

06 Oct '07

Bill Gosper: As nearly as I can tell without more careful work, I have found an arrangement of your twelve disks inside the oval. It's not a strictly kosher solution, however, because there are definitely two non-triangular interstices. (Of course I concede that my somewhat sloppy cutting and fitting may have led me astray.) The graph in the attached file depicts the candidate solution. The disks are named 1 to 12 in increasing order of size. The existence of an edge in the graph between two disks implies that they are mutually tangent, and the absence of an edge implies that they are not. Alan Schoen

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[math-fun] A fractal seq +/- 2007 (bis)
by Eric Angelini 04 Oct '07

04 Oct '07

More (in french) here: http://www.cetteadressecomportecinquantesignes.com/FractAdd.htm Best, É. -----Message d'origine----- De : Eric Angelini Envoyé : jeudi 4 octobre 2007 16:01 À : math-fun Objet : A fractal seq +/- 2007 Hello Math-Fun, if you erase all terms hereunder which are the sum of the two previous terms, you'll get the original sequence. Will the term 2007 appear some time? And if yes, at what index? Best, É. 0,1,1,1,1,2,1,2,3,1,2,3,3,1,4,2,3,5,3,1,4,4,2,6,3,5,8,3,1,4,4,4,8,2,6,8,3,5,8,8,3,11,1,4,5,4,4,8,8,2,10,6,8,14,3,5,8,... - - - - - - - - - - - - - -- - - -- -- -

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[math-fun] nuclear pennies / archimedes codex / indian clerk
by Thane Plambeck 04 Oct '07

04 Oct '07

1) Nuclear pennies, a game on a semi-infinite strip http://sigfpe.blogspot.com/2007/09/arboreal-isomorphisms-from-nuclear.html later on, the blog entry devolves into a discussion of functional programming, Haskell, and monads, but still, interesting 2) I'm enjoying this recent book by Reviel Netz and William Noel, The Archimedes Codex: http://www.amazon.com/Archimedes-Codex-Reviel-Netz/dp/030681580X 3) The recent book by David Leavitt, "The Indian Clerk," a novel about Hardy and Ramanujan, is fun too http://www.amazon.com/Indian-Clerk-Novel-David-Leavitt/dp/1596910402/ -- Thane Plambeck tplambeck(a)gmail.com http://www.plambeck.org/ehome.htm

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[math-fun] A fractal seq +/- 2007
by Eric Angelini 04 Oct '07

04 Oct '07

Hello Math-Fun, if you erase all terms hereunder which are the sum of the two previous terms, you'll get the original sequence. Will the term 2007 appear some time? And if yes, at what index? Best, É. 0,1,1,1,1,2,1,2,3,1,2,3,3,1,4,2,3,5,3,1,4,4,2,6,3,5,8,3,1,4,4,4,8,2,6,8,3,5,8,8,3,11,1,4,5,4,4,8,8,2,10,6,8,14,3,5,8,... - - - - - - - - - - - - - -- - - -- -- -

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