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[math-fun] Help with a recursion
by Bernie Cosell 28 Jan '03

28 Jan '03

I know that I'm getting senile, and I'm growing to accept that, but... this little problem has been driving me *NUTS*. The problem whizzed by on another mailing list as a programming problem and I wasn't particularly interested in the programming aspect [which was actually simple enough given the right algorithm] but in the derivation of the algorithm... But I just *can't* do it, and so I'm looking for some help. I *must* be missing something because it just can't be as hard as I'm finding it. Here's the problem: You want to wager on the outcome of a multi-game [best n out of 2n-1] series, but your bookie will only allow bets on individual games. For a one-game series, this isn't an issue, obviously. But what I was surprised to see was that: For a best two-out-of-three, if you wager half what you want to risk [call that 'R'] on the first two games, then either the series is over and you've gotten the result of wagering R on the series, or the series is tied *and*you're*even*, so you just wager R on the last game and you're done. No matter what happens in the invidual games of the series you win or lose R. For a best three out of five series, it is actually easy enough to do a similar analysis brute force: Bet B on the first two games. If the teams split the series is now best two-out-of-three, and you're even, so use the above strategy. If either time wins both, then you're either ahead or behind by 2B. To make your overall position be 'R' if the same team wins the third game and sweeps, you need to bet R-2B on the third game. If the series goes on, it is now 2-1. But 2-1 in which a five game seeries is the *same* as 1-0 in a three game series and we know how the bets go in that: when a three-game series is at 1-0, you should be ahead [behind] by R/2. Since your current standing is [+/-](4B - R), you just set: R/2 = 4B - R and you solve for 'B' and find out that your first bet in the three out of five series should be 3R/8. It seems that this should just be a high-school simple recusion problem, but it is sure beating me -- I can't even find the brute-force solution for a best 4-out-of-7, much less the general formula for an arbitrary series. It is easy enough to show that all you need is to know the *first* bet -- given just the first bet for a particular series it is easy to figure out ALL the bets for that series, but I'm stuck on how to do that. Insight would be appreciated! :o) /Bernie\

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[math-fun] moving from academia to industry...
by wouter meeussen 28 Jan '03

28 Jan '03

more of you should consider it: it's a win-win proposal : the average intelligence of both populations increases! ;-)) Wouter.

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[math-fun] cell phone math
by Thane Plambeck 28 Jan '03

28 Jan '03

>From a Reuters news story today, "Cell Phones 'Blind' Drivers" Writing in the March issue of the Journal of Experimental Psychology: Applied, Strayer's group said use of a cell phone clearly distracted the drivers.... "It is like studies that show 90 percent of people think they are better-than-average drivers. Forty percent of them are wrong." Thane Plambeck 650 321 4884 office 650 323 4928 fax http://www.qxmail.com/home.htm

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[math-fun] Test
by David Wilson 27 Jan '03

27 Jan '03

Test message

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[math-fun] I'm Back
by David Wilson 27 Jan '03

27 Jan '03

At the behest of my wife, I have resubscribed to math-fun, and am hoping to resubscribe to seqfan if I can get O. Gerard's address. I do not wish to be an OEIS editor, however. I do have comments on A055480. The energetic numbers are numbers that can be broken into substrings and expressed as a sum of powers of those substrings. For example, 8833 = 88^2 + 33^2 is energetic according to the example given in the sequence. If only one substring were allowed, then every number would be energetic, e.g, 44021 = 44021^1. Therefore we must assume that the number must be broken up into at least two substrings, in which case, the numbers 1 through 9, originally included in the sequence, should be omitted. Here is my updated/extended version of this sequence. %I A055480 %S A055480 24,43,63,89,100,101,102,103,104,105,106,107,108,109,132,135,142,153,175, %T A055480 209,224,226,262,264,267,283,284,332,333,334,357,370,371,372,373,374,375, %U A055480 376,377,378,379,407,445,463,518,568,598,629,739,794,809,849,935,994,1000 %N A055480 Energetic numbers. %O A055480 1,1

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RE: [math-fun] building an on-line math museum
by Kimberling, Clark 27 Jan '03

27 Jan '03

Ed (and others), Right on! Sketchpad (version 4) is a wonder - and so is the "automatic" JavaSketchpad. May I ask you to visit http://faculty.evansville.edu/ck6/GIAJSP/ . The interactive action-sketches show some things that can be done with the Version 4 JavaSketchpad much more readily than with Version 3. This is a new site, so there are bound to be things to be improved. Ed, if you or others visit the site and see errors or other opportunities for improvement, please let me know (ck6(a)evansville.edu) (The site cited above, called "G.I.A. Java Gallery", is associated with a book, Geometry in Action, released this month from Key College Publishing.) Thanks, Clark Kimberling -----Original Message----- From: ed pegg [mailto:ed@mathpuzzle.com] Sent: Sunday, January 26, 2003 6:32 PM To: math-fun(a)mailman.xmission.com Subject: RE: [math-fun] building an on-line math museum > >>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. The first thing he should pick up is Geometer's Sketchpad. It's pretty effortless to go from a geometric construction, as in the triangle to square dissection, to a fully functional java applet. Really, it's just draw and save an applet. Geometry in Motion has examples: http://www15.addr.com/~dscher/ There are many good math sites out there. He should look at all the sites presented as columns at http://maa.org/news/columns.html . My site, mathworld.com, and Erich Friedman's site all have much more, especially in the way of links to much more. --Ed Pegg Jr. _______________________________________________ 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] 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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