March 2006 - mathfun@mailman.xmission.com

Re: [math-fun] batting averages
by Michael Reid 27 May '06

27 May '06

> SHOULDA > wrote: > At minimum, > (c74) block([keepfloat:true],linsolve((2*integer+1)/(5*integer+3)=0.3985)) > > (d74) [integer = 26.066] > > (c75) subst(ceiling(%),5*integer+3) > > (d75) 138 > Serves me right for not using continued fractions. > at bats. ok, that looks better. but how do you get the form (2n + 1) / (5n + 3) ? is there some way without continued fractions? btw, the c.f. method i described before can be cleaned up slightly. to find the "simplest" rational number in the closed interval [a, b] , compute the convergents for the cf's of a and b . suppose p/q and P/Q are the last two they have in common. then the next convergent for each will be of the form (p + Pn) / (q + Qn) for some positive integer n . if the simpler of these two is in the target interval, then that's the one. otherwise, replace n by n+1 in its expression as above, and that gives the simplest fraction in the interval. (this may require a and b to be positive, but it's easy to reduce to that case.) mike

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[math-fun] Problem Puzzler 1999
by Christian Boyer 10 May '06

10 May '06

Jean-Paul Delahaye publishes in the new issue of Pour La Science a very interesting article on Sudokus. He asked a very strange Sudoku problem WITHOUT any given numbers, only ">" and "<" signs between cells. He mentions that this problem was published in Puzzler, 1999, and that he does not know the solution. I have the solution, sent this morning to J.-P. Delahaye. Now looking for "Puzzler 1999" on Google, I find that Ed Pegg Jr. wrote an article in September 2005 including the same astonishing puzzle, figure 7 "Greater Than Sudoku" in: http://www.maa.org/editorial/mathgames/mathgames_09_05_05.html Perhaps that somebody else had already the solution? Ed, did you receive a solution to your article? Christian.

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[math-fun] moderator outage; math undergrad rec?
by Schroeppel, Richard 02 Apr '06

02 Apr '06

I'll be away for a week. Play nice. ---- A daughter of a family friend is about to select her college. She likes math, so I want to recommend some good undergraduate math programs. My own experience is 40 years out of date. Back then, MIT provided an excellent undergrad math program, in spite of their overall neglect of undergrads, and a sink-or-swim attitude. (Maybe I should rephrase that to "the survivors got a good math education".) Anyway, I'd like some more up to date information. Rich

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[math-fun] Pandiagonal Sudoku?
by Christian Boyer 01 Apr '06

01 Apr '06

Do you know if a pandiagonal Sudoku has already been published? I have a 25x25 example, the smallest possible size for this problem, but perhaps the same work has already been done. "Pandiagonal Sudoku" means that all the diagonals and broken diagonals of the square should also contains all the numbers, as it is for rows, columns, and sub-squares. It is proved that a pandiagonal Latin square cannot exist for 2k and 3k orders, meaning that a pandiagonal Sudoku of standard size (9x9) is impossible. I know published 25x25 pandiagonal Latin squares, but they are not Sudokus, because they are not organized in 5x5 sub-squares. Christian.

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[math-fun] Sum of reciprocals of 8877690 integers with distinct digits
by Robert Baillie 30 Mar '06

30 Mar '06

Problem E2533 in the American Mathematical Monthly (1975 or 1976) says there are 8877690 integers that have distinct digits. The problem is to estimate the sum of their reciprocals. I thought I read someplace that someone had computed the exact sum. Does anyone know how big the numerator and denominator are? And, by the way, what is the approximate sum? Bob Baillie

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[math-fun] Road Sign Math
by Henry Baker 29 Mar '06

29 Mar '06

http://www.roadsignmath.com/

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[math-fun] Mathematics as Hypertext ... and a Logic Assistant
by Guy Haworth 29 Mar '06

29 Mar '06

I'm contemplating two projects for final-year CS students to do: 1) Thinking of mathematics as (partly comprising) a set of: Theorems with Preconditions and Proof(s), Generalisation theorem-theorem relationships, Theorem-(used in/by)-Proof relationships Counterexamples ... I see this information forming a database with an application 'projecting' this information to a web-interface which allows one to navigate around 'theorem space'. This seems well-suited to the web, and the opportunities of multimedia (graphics, animation, video, sound) is just a bonus - perhaps helped also by the XML-style language MathML. I'm thinking of asking a CS student to create such a system. Question is - is there anything out there of this kind already? 2) The intended system is a 'Logic Assistant'. A user-student would be trying to prove something using the formal means of a logic with already-known results and rules of inference. The system would either know the proof (as provided data) or be trying to work it out too [and I think there are systems for this 'out there' but I don't know about them]. The student would start with say 100 points and lose a few points for every 'atom' of hint provided by the system. The system would be able to manage hints, compare what the student proposed with the right answer, and general be an assistant/mentor/tutor in the learning process. Same question as for '1' really - is there anything out there of this kind already? Thanks in advance for any inputs - Guy Haworth, Univ of Reading, UK

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[math-fun] Mathematica Guidebooks ?
by Robert Baillie 27 Mar '06

27 Mar '06

Springer publishes a 4-volume set of Mathematica reference books by Michael Trott, at $80 per volume. They are described at http://mathematicaguidebooks.org Has anyone seen hard-copies of these? What do you think? Are they useful? Are they a waste of money? Bob Baillie

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[math-fun] F-Secure vs mfarch?
by R. William Gosper 27 Mar '06

27 Mar '06

I read mail over a link to unix, and have *never* had a virus. I de- installed Norton for its uncontrollable popups, surfing naked for a few days due to 15hr dialup download for F-Secure. Finally got it, thanks to Ed Hudson. First scan reported three unspecified viruses, then died in an infinite loop while reading mfarch/math-fun-archive-950622-960702 ! Really died. Not even killing the window killed the looping process. So I rebooted and just scanned mfarch. Two viruses reported, then the same death. I buzzed through the whole file with emacs. Nothing amiss. So I punted F-Secure and downloaded Panda, which ran ten times faster, deleted a bunch of cookies, and also excised the raw text of some classic viri from some ancient inboxes that I knew were "infected" and only open with emacs. (Norton, Trend, and F-Secure missed these, perhaps deliberately.) Panda did not attack the virus definitions presumably in the F-Secure download (which survived the deinstall) nor anything in mfarch. Does anyone else have F-Secure and mfarch? Do I have an incredibly subtle virus whose purpose is to embarrass F-Secure? --rwg DELUSIONAL OULED-NAIL'S ANDOUILLES

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[math-fun] Mandelbrot Set: the song
by James Propp 27 Mar '06

27 Mar '06

Check out the song "Mandelbrot Set" by Jonathan Coulton: http://www.jonathancoulton.com/lyrics/mandelbrot-set Sample of the lyrics: "Mandelbrot's in Heaven, at least he will be when he's dead / Right now he's still alive and teaching math at Yale..." (Would that make New Haven the opposite of Heaven?) ;-) Jim

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