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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 05 Oct '07

05 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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[math-fun] well known but no references?
by Anna Johnston 04 Oct '07

04 Oct '07

A last minute talk was given this year at the Finite Fields and their applications conference (http://www.deakin.edu.au/scitech/eit/fq8/) claiming to break several discrete logarithm based public key cryptosystems. Their break consisted of basing the cryptosystems in Z/(p^n)Z where the discrete logarithm was known in Z/pZ. I had thought that this was a well known result, just a simple extension of Hensel lifting (it's a fun number theory exercise to work out the details), but haven't found any references to 'exponential Hensel lifting' in any of the usual places. Google turned up nothing either. Does anyone know of any references to this? Amy Johnston

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[math-fun] Re: Mathpedia/Wikiproof
by Steve Witham 03 Oct '07

03 Oct '07

>From: "Joshua Zucker" <joshua.zucker(a)gmail.com> > >Maybe my experience is too many years out of date, but I find >computer-understandable proofs to make them much less accessible in >general. For instance, in geometry you need to use something closer >to Hilbert's approach, and spend (waste?) lots of time on proving that >this point is between those two, or this ray is between those two, so >you can add or subtract distances or angles. Of course, it's >essential to prove those things to make proofs rigorous, but rigor and >accessibility are quite different things, and I think negatively >correlated. The problem is similar to that of writing good computer programs. But they are like cousins long out of touch. With programming, I think clarity correlates with rigor--but that's in a situation where both are up to the style or preference of the programmer. As with all programming disciplines, a lot depends on whether one has got religion oneself or is being dragged into it. (I could see wikiproof politics going either or both ways.) Math at least has the advantage that proofs tend to be aired by publication. What I mean by rigor is that the programmer worked to be sure they covered all the cases. I think thoroughness correlates with clarity because un-clarity provides places where bugs can hide--it's a bit different with computer validation, but probably clarifying (better organization) is one of the best ways to debug (i.e. satisfy a verifier about) proofs. There is an old study where one group of programmers was told to write a program to be clear, another group, to be fast. The programs written to be clear turned out at least as fast as the "fast" ones. The Qedeq language ( qedeq.org ) looks good in concept with its syntactic sugar and libraries. There could be a form of stretchtext where the justifications of some steps are hidden but clickable (or selectively hideable). My impression is that mathematicians think of a lemma as either a special move like a fancy gymnastic dismount, or a sign that a problem is a really big one. Early in the history of computers subroutines were considered costly and thought of in similar ways. Whereas lately one is encouraged to always break things down. In some languages (e.g. forth) primitives and subroutines are on equal footing and it's considered a sin to write any program longer than a single sentence without breaking it into smaller subroutines (imagine a single dictionary definition going on for a page). Prolog programs that I've seen tend to have very short statements. Long proofs read like the unstructured programs of yore. >Working with automated proof checking sounds painful. "Double-entry bookkeeping? Audit trails? I don't likes the sound o' that!" Just the fact that it seems awkward is an interesting symptom that makes it worth persuing. It's as if we lived in an era where long calculations were carried out by rare experts' hands. Math is very steampunk, including all the funky typography and ancient alphabets. Calculemus, I say. http://www.tiac.net/~sw/2003/08/calculemus.html --Steve

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Re: [math-fun] Mathematical cosmos article by Max Tegmark
by Dan Asimov 01 Oct '07

01 Oct '07

<< So, yes, Max is correct, but only vacuously so. This conclusion also strikes me as correct, but vacuously so. --Dan

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