January 2003 - mathfun@mailman.xmission.com

[math-fun] building an on-line math museum
by James Propp 26 Jan '03

26 Jan '03

David Gale (gale(a)math.berkeley.edu) who served as editor of the Mathematical Entertainments column in the Intelligencer before Michael Kleber and Ravi Vakil took over the post, is thinking of putting together an on-line museum of mathematics. He's interested in finding out about existing sites that are highly interactive and whose mathematical content is elementary. Can any of you provide links? He's also interested in creating some new software (or rather having someone create it to his specifications). Here is the text of a message that he posted, requesting help on a specific project: >To: students in mathematics, computer science, operations research > >I am interested in finding someone who might want to work on software for >an interactive web site intended to illustrate some mathematical aspects >of a problem in geometry and tiling. The details are described in the >attached file. The work will pay at the rate of $15 per hour and there is >also the possibility of receiving units' credit (in mathematics) as >independent study. > >This project would be part of an effort to create an on line web site >whose purpose would be to introduce members of the general public to some >of the fascination connected with the subject of mathematics. There is >already a great deal of this sort of material scattered around on the >internet. After many hours of surfing I found a few examples which may >give an idea of what I have in mind. > >1 Among the dozens of interactive proofs of the Pythagorean Theorem this >one seemed among the simplest and most elegant. > >http://www.studyworksonline.com/cda/content/applet/0,,NAV2-21_SAP696,00.sht… > >2. To see mathematics applied to a familiar real life situation the >so-called sorting problem seems a natural. The following is suggestive >although a much more elementary and interactive version could be made. I >am planning to try to put together such a package. > >http://cs.smith.edu/~thiebaut/java/sort/demo.html > >3. Same comments as above applies to this rather pretty three-body applet > >http://www.ifmo.ru/butikov/Projects/Collection.html > >4. Below is a good example of an interactive exhibit although >unfortunately it has nothing to do with mathematics. > >http://www.exploratorium.edu/exhibits/mix_n_match/ > >The purpose of the exhibit described in the attached file would be in part >to serve as a prototype of the sort of thing I am looking for. If after >reading the accompanying description of the project you think you might be >interested in working on it please contact me, telling me a little about >who you are. > >David Gale, >Professor Emeritus, Mathematics >UCB The file that he attached to this message, describing a particular piece of software that he wants someone to create, is on my web-page at http://www.math.wisc.edu/~propp/hidden/dissect.doc Jim Propp

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[math-fun] 150 birthday of ricci-curbastro
by Thane Plambeck 25 Jan '03

25 Jan '03

I thought this was interesting, in the 9 January 2003 Nature Magazine "50 years ago" column: * * * * Gregario Ricci-Curbastro, inventor of the tensor calculus, was born at Lugo, in Italy, on January 12, 1853. The absolute differential calculus, as he himself called it, gained little attention until Einstein used it for the formulation of general relativity, even though it had reached a mature form by 1895, after some ten years of growth. It was so little thought of, indeed, that in 1901 Ricci was denied the Italian Royal Prize in mathematics on the ground that the calculus was "useful but not essential for the treatment of some mathematical questions." Nevertheless he himself retained a belief in its value... In 1912 Einstein's attention was directed to it by his colleague, Marcel Grossman, and the outcome was the relativistic theory of gravitation published in 1916...The relativistic principle of covariance, namely, that the general laws of physics can be expressed in a form which is independent of the co-ordinate system, has a meaning only in so far as there exists a way of expressing them in such a form. The Ricci calculus provides a means of doing so...The tensor calculus is fully established as one of the main instruments of modern mathematics, and gives its inventor a permanent place in the history of the subject. [From Nature, 10 January 1953] Thane Plambeck 650 321 4884 office 650 323 4928 fax http://www.qxmail.com/home.htm

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[math-fun] Re: your mail
by Richard Guy 24 Jan '03

24 Jan '03

I'll make a wild guess that it can be proved that no such n exists; I'll copy this to some people who may be able to confirm or deny this. R. On Wed, 22 Jan 2003, Mr. Nayandeep Deka Baruah wrote: > Dear Professors Guy and Borwein, > > I would like to know from you whether the following result is still a > conjecture or has been proved by somebody. > > There exists a composite integer n such that for each prime divisor p of n > (p+1)|(n+1). > > If it is true then what is the smallest such number? Are such numbers are > infinitely many? > > I would be extremely grateful for your help. > > With best regards, > > Nayandeep Deka Baruah > Dept. of Math. Sciences, > Tezpur University > Napaam-784028 > Assam, INDIA.

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[math-fun] permutable ("absolute") primes, again
by R. William Gosper 24 Jan '03

24 Jan '03

Recall Sloane's old request for more terms of A003459 2 3 5 7 11 13 17 31 37 71 73 79 97 113 131 199 311 337 373 733 919 991 and Rich's astonishing observation that the next term is 1111111111111111111. Absent Rich's analysis, trying to extend this sequence makes a great set of beginner's programming exercises. Of course, we can't expect to reach (10^19-1)/9, but we can at least see how far we can push the bound. As I explained to a 7th grader, even restricting the search to combinations of the four digits 1,3,7,9 entails numbers like 4^18 ~ 10^11. But the 7th grader is at this very moment having heart surgery, and to keep occupied, I added some speedups to our search program: only look at starting numbers with nondecreasing digits, and generate only unique digit combinations, and only as needed. (We get the target sequence afterward by generating and merging the various permutations, and fudging the initial 2,3,5,7.) To my amazement the (uncompiled, Macsyma) program printed 11,13,...,199,337, and after about a minute, 1111111111111111111 ! And after a few more minutes, (10^23-1)/9 ! Here's hoping the 7th grader wakes up with enough neurons to appreciate why these speedups are way bigger than they initially seem. PS, I seem to have lost the mail with Rich's proof. Where are the old archives?.

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[math-fun] Matthew Cook and his proof about Rule 110
by asimovd＠aol.com 22 Jan '03

22 Jan '03

Harold writes: << ... Cook's web page at CalTech has been "disappeared" (replaced by a "FORBIDDEN" notice, that is)... >> Can anyone explain how a mathematical theorem can be protected intellectual property? If there's one thing I thought I knew about intellectual property law, it was that *ideas* per se could not be protected. I've never heard of another situation where a theorem was considered proprietary. --Dan

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[math-fun] another ANKoS review
by Richard Schroeppel 21 Jan '03

21 Jan '03

[Thanks to Paul Chapman on the Life list for pointing this out.] Larry Gray's review of Wolfram's ANKoS is available online at http://www.ams.org/notices/200302/fea-gray.pdf This is a much more useful review than the previous AMS screed. It points to some of the useful ideas in the book, and doesn't get carried away with criticism of Wolfram. It also mentions a half dozen other reviews, with one sentence summaries. Rich rcs(a)cs.arizona.edu

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[math-fun] "Beal's Conjecture"
by Steve Gray 18 Jan '03

18 Jan '03

I thought this comjecture was relatively new, following Wiles' proof of FLT. But it is discussed, not in connection with Beal's name, in 1968. See "On Solutions of the Equation x^a + y^b = z^c" in Mathematics Magazine, 1968, p. 174, by Allan I. Liff, who presents some facts and conditions on its solution. I think the usual notation now is a^x + b^y = c^z. So far as I know, in all solutions found so far, one of x,y,or z is 2. Steve Gray

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[math-fun] Ideal polygons in the hyperbolic plane
by asimovd＠aol.com 17 Jan '03

17 Jan '03

In the Poincaré model, the hyperbolic plane H is viewed as an open unit disk D in the (ordinary) plane, with the geodesics being any arc of a circle that's perpendicular to the circular boundary bd(D). For any geodesic polygon in H, its area is A = [sum of its exterior angles] - 2 pi. One can also have ideal (geodesic) polygons, all of whose vertices lie on "the circle at infinity", i.e., bd(D). Since each exterior angle of such a polygon must be pi, its area is a function only of the number of sides N: A = (N-2) pi. Also, all the sides of an ideal polygon are of infinite length. QUESTION: When are two such ideal hyperbolic N-gons isometric (i.e., congruent in H) ? Note that the space of all such N-gons is N-dimensional (depending on the vertices on bd(D), whereas the group of isometries of H is the same as the group of conformal (or anti-conformal) automorphisms of D -- a 3-dimensional group. Hence there are N-3 dimensions of congruence classes of such ideal N-gons. >From this it's easy to see that all ideal triangles in H are congruent. Given the 4 vertices on bd(D) of each of two ideal squares in H, what's a concise algorithm to determine whether the two squares are congruent? --Dan

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Re: [math-fun] Copyright extension
by Dan Hoey 16 Jan '03

16 Jan '03

> Dan, > There seems to be a considerable interest in this topic. If it leaves you > cold, why not just delete the posts with subject line as above? > Regards, > Dan I'm sick and tired of mailing lists, newsgroups, and any other discussion forum turning into outlets for misinformation, posturing, poseuring, and vapid speculation on this topic. I did not subscribe to math-fun to listen to yet another copyright spew. It's not math, it's just something that EVERYONE has an opinion on, not just mathematicians. You don't think math-fun is the first place it's happened, do you? Copyright arguments EAT discussion groups. If you're so interested in getting misinformation on copyright, why aren't you reading misc.news.intellectual-property, or whatever it's called, on Usenet? You can get much greater quantities of opinions, with the same level of unreliability. And people there won't be asking "where's the math?" because those people are reading a newsgroup devoted to copyright opinionizing, not one they are reading for the math. Dan

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[math-fun] Re: Manners
by Dan Hoey 16 Jan '03

16 Jan '03

Joshua Singer <singer(a)stanford.edu> thinks my tone is uncalled for. Well, my tone expresses my discomfiture at having to endure this topic, argue against this topic, or both. Someone here might have the mistaken impression that I enjoy arguing against copyright discussions as much as I dislike the discussions themselves. No, I hate and abhor having to remind people that I'm here for the mathematics and not for extended discussions of other topics. I will not enter into any further remonstrations with people who misuse math-fun with discussions of what copyright law is and should be. If it continues beyond my tolerance, I will just unsubscribe. I like reading about math. I am not willing to subscribe to a copyright discussion group to do so. And if anyone tells me "just hit delete" again, I suggest you subscribe to sneh-lovers and see how many times you can hit delete before you've had enough. But I find it difficult to respect anyone's argument for the continuation of this discussion on math-fun. It's not like there aren't places where you can get copyright discussions, all copyright discussions all the time, and the people there are there for the copyright discussions. It's not like the you're going to find anyone posting to math-fun with any special expertise in the subject, or with any great potential for changing the status quo. In fact, the choice of math-fun as a venue for copyright discussion practically ensures that you are going to get half-baked opinions from people who don't know much about copyright, haven't thought through what they do know, and don't have a better outlet for their witless maunderings than gassing in e-mail. Forgive me if anyone who posted here actually _is_ a copyright lawyer, or legislator, or treaty negotiator, or pressure group runner. It certainly sounded like gas to me. And as for it being a popular topic, how about great sex? Everyone's interested in great sex. Let's have a discussion about our sexual experiences, fantasies, aspirations, and phobias, and by all means let's do it in the road on math-fun. And does anyone want to discuss the war on drugs on math-fun? I understand war is hell, but maybe it's more enjoyable on drugs, and I'm sure someone on math-fun has an opinion. How about Nu-Skin--I understand you can make more money with it than Amway, and if your friends turn against you, at least their skin is soft. What does math-fun think about international funds transfer, penis enlargement, collecting pop-tops for kidney transplants, the source of the phrase "rule of thumb", Joe Boxer, Joe Millionaire, Joe Camel, and Joe Pye Weed? Have you ever tried looking in the yellow pages, deleting ninety-eight or ninety-nine of every hundred words, and trying to make a theorem out of what is left? Would you like to try that with math-fun? I wouldn't. You know, I was just now working on the mathematics of Bingo, and here I have to leave for the weekend. Well, have a good one, and I'll see you all in some mathematical venue. Dan

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