June 2010 - mathfun@mailman.xmission.com

[math-fun] My wife + math
by Jason 29 Jun '10

29 Jun '10

My wife just posted this to her blog: ---- I think I'm falling in love with math. I mean, I always liked math, but we were never more than just friends. As I really get to know it better, things that used to be charming become irresistible. I can't stop thinking about it all day! It feels like my brain was never really turned on like it is right now. Don't worry, J. You'll always be my one and only. Besides, this may just be an infatuation. ;) We'll see how things go when I hit Calculus and math suddenly changes on me. . . ---- She always did well in math, and had a friend/rival in elementary school who she always competed with to be the best in her math studies. Then in about 9th grade, her teacher wouldn't let her move on to the fast track because she hadn't done enough homework to get an A, even though she was acing the tests. Apart from feeling cheated, she was now also behind in the expected progression for technical fields. She studied English in college, and never got past college algebra. Now she's back in school, thinking of doing a graduate degree in engineering. So she's at the community college, where she's supposed to take several years worth of prerequisites outside her final department, to get the math and science core she feels like she needs just to apply to a good grad school. Likewise, my cousin loved astronomy in high school, where they had a neat research-oriented pilot program. Her project was to study historical photos of nebulas to see if expansion could be tracked over decades. I encouraged her to take more when she got to college, but when she saw how many math and other science classes she'd have to take as prerequisites, she also decided to major in English. One last related anecdote: I just met Sridhar Vembu last weekend. He found such a brain drain from the indian universities that he had trouble hiring for his indian software company. So he started a trade school. He takes 17-year-old poor kids with interest and a cursory hint of aptitude, and teaches them programming (while giving them a stipend and feeding them). The curriculum covers programming, english and math in that order of importance, and in that order of preference. The kids hate abstraction and math notation, but later appreciate it more after they've spent a few months solving practical problems in web programming. After 6-9 months, almost all of them start working for the company (they lose some conservative muslim girls to being married off by their families), and do just as well as the college grads. As he puts it, "math is the new sanskrit". Oh, and I believe he's taking about half and half girls/boys. (Except that more of the girls get recruited away by the colleges.)

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Re: [math-fun] Intuitively simple trig functions
by Dan Asimov 25 Jun '10

25 Jun '10

Mike wrote: << Is there a geometric way to understand the Taylor series for sin and cos? The closest I've been able to find is a combinatorical explanation (below), but it doesn't seem to help much. >> I'd love to know such a way to understand their Taylor series. I recently gave a talk to a bunch of smart youngsters about complex numbers, and was unable to find a truly graceful way to explain why exp(ix) = cos(x) + i sin(x), (without deriving their Taylor series). So if anyone knows a way to see this, I'd love to know it. But of course that would require giving exp a meaning on the imaginaries. Mike continued: << The paper "Objects of Categories as Complex Numbers" by Marcelo Fiore and Tom Leinster and says that under certain conditions, objects can behave as though they had complex cardinalities. It turns out that data types of typed programming languages satisfy the conditions; the data structure T = T^2 + T + 1 of trees with 2 (ordered), 1, or 0 children, behaves like "i". It is not the case that T^4 is isomorphic to the one-element set, but T^5 = T. Since it's a countably infinite set, this may seem obvious, but there's a way of constructing the isomorphism using only distributivity and the defining isomorphism above, so the cardinality is also preserved. . . . . . . >> I don't really understand this, but it sounds fascinating. --Dan ________________________________________________________________________________________ "Outside of a dog, a book is man's best friend. Inside of a dog, it's too dark to read." --Groucho Marx

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[math-fun] Conway Life in the News
by Dave Dyer 25 Jun '10

25 Jun '10

There's a good article in the current New Scientist about Conway's Life, inspired by the recent development of a self-replicator dubbed "Gemini" http://www.newscientist.com/article/mg20627653.800-first-replicating-creatu… Also, there's the forum where the discovery was announced, which has a very good compendium of past and present life activity. http://conwaylife.com/

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[math-fun] Fairly concise R-R CF in theta constants
by Bill Gosper 24 Jun '10

24 Jun '10

Arcsinh of (the same) four thetas, twice. http://gosper.org/R-R CF.pdf Anyone have a shorter expression? Can anyone convince Mma to Series the rhs? --rwg

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[math-fun] Cryptic
by Thane Plambeck 23 Jun '10

23 Jun '10

http://www.guardian.co.uk/crosswords/cryptic/25044 Tippy-tapped on my iPad

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[math-fun] Fwd: Special Martin Gardner issue of The College Mathematics Journal
by rcs＠xmission.com 23 Jun '10

23 Jun '10

----- Forwarded message from cmj(a)oberlin.edu ----- Date: Fri, 18 Jun 2010 15:21:36 -0400 From: CMJ <cmj(a)oberlin.edu> Reply-To: CMJ <cmj(a)oberlin.edu> Subject: Special Martin Gardner issue of The College Mathematics Journal The College Mathematics Journal is planning a special issue devoted to Martin Gardner’s mathematics. I’m writing to you as someone actively interested in Martin Gardner’s work. Below is pasted in a call for submissions for that issue. Of course I hope that you will submit a paper, but I ALSO hope that you will pass this invitation on to other mathematicians (recreational and otherwise) whom you think might be interested. If you prefer, please send me the names of any mathematicians whom you think should receive the Call for Papers, and I will send them a copy. best regards, -Michael- PS. I’ll be at MathFest in Pittsburgh this August and would be happy to discuss this special issue of CMJ and any potential submissions. -M- Michael Henle, editor The College Mathematics Journal cmj(a)oberlin.edu CALL FOR PAPERS Submissions are sought for the January 2012 issue of The College Mathematics Journal which will be devoted to the mathematics of Martin Gardner. Papers submitted should be short (4-10 pages in manuscript: standard letter sized sheets, double-spaced, 12 point type) and address a topic that Martin Gardner introduced in one of his Mathematical Games columns for Scientific American. In outline, papers should briefly give the history of Martin Gardner’s involvement with the subject of the paper and then go on to describe a contemporary development from that topic. In order to avoid duplication of effort, authors are strongly encouraged to write the editor of CMJ (at cmj(a)oberlin.edu) describing their proposed paper. Final submissions must be received by February 1, 2011 to be assured of consideration for this issue. ----- End forwarded message -----

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[math-fun] Numberplay
by Bernie Cosell 22 Jun '10

22 Jun '10

I just discovered that the NYTimes "Wordplay" blog [which I find to be pretty much a bore and so don't look at] has been running a "Numberplay" column on Mondays. The column from yesterday, the 21st, is at: <http://wordplay.blogs.nytimes.com/2010/06/21/numberplay-spooky-action- at-a-distance/> You can access all the Numberplay columns via <http://wordplay.blogs.nytimes.com/category/Numberplay/> /Bernie\ -- Bernie Cosell Fantasy Farm Fibers mailto:bernie@fantasyfarm.com Pearisburg, VA --> Too many people, too few sheep <--

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[math-fun] invertible nearly-linear integer functions
by Steve Witham 22 Jun '10

22 Jun '10

For any real k >= 1 and any int x, round( round( k x ) / k ) = x That's really simple and really wasn't obvious to me. Quikproof: whether or not k = 1, | kx - round(kx) | / k < .5. This extends to x in Z^n, since everything applies componentwise. Mathematically, if k >= 1, x |--> round( k x ) is injective (a.k.a. "one-to-one") but not bijective (I'm cribbing from wikipedia). But computer science-wise, it's "invertible," meaning it's injective and... reasonably easy to compute the exact inverse of a point that has an inverse. So now I'm slightly wiser about the terms "invertible" and "one-to-one function". I focused down to that simplest example while reading, "A global method for invertible integer DCT and integer wavelet algorithms," by Gerlind Plonka. More generally for any given orthogonal matrix A like a Fourier transform, there's a constant k such that for any int input vector x, F( x ) = round( k A x ) round( 1/k A^-1 F( x ) ) = x What's important about that is that F(x) gets closer to the true transform than doing individual butterflies (say) in a reversible integer way. Yet it seems to me that if k >> 1, this expands the frequency-domain numbers so they require...some constant number more bits each, sort of pyrrhic in the background context, which is compression. So, reading on. --Steve

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[math-fun] Nonobvious integer sequence
by Bill Gosper 20 Jun '10

20 Jun '10

8, 56, 996, 1680, 5236, 280, 28, 224, 448, 749196, 728, 980, 420, 112, 1708, 56, 112, 56, 308, 252, 532, 84, 2156, 28, 84, 280, 29260, 140, 6454336, 3220, ... = period of the sequence x[n+1]:= floor(2 cos(2 pi/7) x[n]) - x[n-1], x[0]:= cosh(k)^2, x[1]:= sinh[k]^2. The pi*<rational> suppresses its natural tendency to grow like x0^2+y0^2. --rwg

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Re: [math-fun] And Beano was his name-0
by Dan Asimov 20 Jun '10

20 Jun '10

Marc wrote, to my guesses: << Seems plausible. But, to start with, what evidence is there this person truly existed? Say, for instance, on some Columbia or math genealogy site? >> This is true -- I didn't even find evidence he existed on the math genealogy site, which is pretty strong evidence he never got a Ph.D. Which is one characteristic of many nonexistent people, but I'm guessing that in those days good math depts. often hired non-Ph.D.s along with the Ph.D.s. Contacting Columbia might be the best way to be sure. --Dan Even though kleptomaniacs can't help themselves, they do.

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