December 2015 - mathfun@mailman.xmission.com

[math-fun] Julian pimped my pump
by Bill Gosper 17 Dec '15

17 Dec '15

To run it <http://gosper.org/pumper_2.mp4> continuously, download with Miro, QuickTime-View-Loop. The pumped shapes split lengthwise resemble boats, so a grand entrance to a math museum would be a chain of these boats in an annular canal, passing through four rotors acting as an (approximate) air|water lock, with another four for the exit. Oh, the insurance. --rwg No manual entry for overboard

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[math-fun] The end of the 32-bit computer?
by Henry Baker 16 Dec '15

16 Dec '15

Google's decision to end support for its browsers on 32-bit computers signals the end for 32-bit computers in general. If you can't run a browser, then you can't be a full-fledged computer in the 21st century. Most *serious* computer people have always considered 32 bits to be too small, and therefore a 32-bit computer was always a *mini* computer (at least DEC got this part right). Von Neumann's 1944 EDVAC computer had *44 bit* words, and was therefore a *real* computer: https://en.wikipedia.org/wiki/EDVAC At least 32-1=31 is prime; 64-1=63=3^2*7. 128-1=127 is again prime. But 257=2^8+1 is prime -- the next such after 17=2^4+1. --- Google to end updates, security bug fixes for Chrome on 32-bit Linux http://www.theregister.co.uk/2015/12/02/googles_chrome_32bit_linux/

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Re: [math-fun] Draft of December essay
by James Propp 16 Dec '15

16 Dec '15

I'm writing another Mathematical Enchantments essay and would welcome comments; see https://mathenchant.wordpress.com?p=344&shareadraft=56709c7eb1189 Keep in mind that all comments submitted via Wordpress are anonymous unless you specifically include your name in your comment. (You can also reply by email.) Do any of you know how to create "hover-notes" in Wordpress? I want to set things up so that if somebody moves their mouse to the phrase "the G-bomb", they'll see a message saying "Nobody actually calls Graham's number 'the G-bomb'" Thanks, Jim Propp [Sorry I accidentally hit "Send" when I was still composing this message.] On Tue, Dec 15, 2015 at 6:08 PM, James Propp <jamespropp(a)gmail.com> wrote: > I'm writing another Mathematical Enchantments essay and would welcome > comments; see > https://mathenchant.wordpress.com?p=344&shareadraft=56709c7eb1189 > > Keep in mind that all comments submitted via Wordpress are anonymous > unless you specifically include your name in your comment. (You can also > reply by email.) > > Do any of you know how to create "hover-notes" in Wordpress? I want to set > things up so that if somebody moves their mouse to the phrase "the > G-number", they'll see a message saying "Nobody actually calls Graham's > number >

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[math-fun] Draft o December essay
by James Propp 15 Dec '15

15 Dec '15

I'm writing another Mathematical Enchantments essay and would welcome comments; see https://mathenchant.wordpress.com?p=344&shareadraft=56709c7eb1189 Keep in mind that all comments submitted via Wordpress are anonymous unless you specifically include your name in your comment. (You can also reply by email.) Do any of you know how to create "hover-notes" in Wordpress? I want to set things up so that if somebody moves their mouse to the phrase "the G-number", they'll see a message saying "Nobody actually calls Graham's number

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[math-fun] spigot algorithm
by Warren D Smith 14 Dec '15

14 Dec '15

It seems to me, wikipedia does not really define the concept. How about you propose a better definition?

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[math-fun] Happy Eighth Night Summation
by Hilarie Orman 14 Dec '15

14 Dec '15

May all your math be enlightening on this last might of the festival of triangular numbers. Hilarie

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Re: [math-fun] spigot algorithms
by Henry Baker 13 Dec '15

13 Dec '15

At 12:31 PM 12/13/2015, Warren D Smith wrote: >what is the definition of a spigot algorithm? https://en.wikipedia.org/wiki/Spigot_algorithm

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[math-fun] spigot algorithms
by Warren D Smith 13 Dec '15

13 Dec '15

what is the definition of a spigot algorithm?

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[math-fun] An observation on meanders
by David Wilson 13 Dec '15

13 Dec '15

I was playing with counting meanders, and took a look at the paper http://www.math.uwaterloo.ca/~malacroi/Latex/Meanders.pdf In particular, I was interested in Table A.4, where M^(k)_n (1 <= k <= n) gives the number of closed meandric systems of order n (= 2n crossings) with k components. A008828 gives shows M in lexicographic order on (n, k). >From the development in the paper, we find M^(1)_n = A005315(n) = number of closed meanders of order n. M^(n)_n = A000108(n) = Catalan(n) SUM(k = 1..n; M^(k)_n) = Catalan(n)^2 I found the following empirical relations between elements in the table, which I do not believe are in the paper: M^(n-1)_n = M^(n)_n * (2n(n-1))/(n+2) M^(n-2)_n = M^(n-1)_n * ((n-2)(n^2+7n-2))/((n+3)(n+4)) I strongly suspect these relations hold for all n, A008828 could be used to verify this for a few larger n. I would not know how to prove these. If these relations indeed hold, it suggests that there might be a similar relation between each element in the table and the one above it. If a few more of these relations could be worked out and some pattern found, we might be able to find a formula for A005315 (he said overoptimistically).

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[math-fun] Current state of "Spigot" algorithms ?
by Henry Baker 13 Dec '15

13 Dec '15

What is the current state of "spigot" (Borwein-type) algorithms for transcendental numbers? Are there only a handful of such algorithms for specific numbers, or are there some classes of numbers -- e.g., log(some-expression), sin(some-expression) -- which have "parameterized" spigot algorithms? I'm looking for a relatively short (1-2 sentences) and/or links that might have the answer. I want to mention "spigots" in passing while talking about random number generators.

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