July 2010 - mathfun@mailman.xmission.com

[math-fun] reciprocal mod 100
by rcs＠xmission.com 07 Jul '10

07 Jul '10

Q: What's the reciprocal of 33 mod 100? Hint: Add 64. When N ends in 3, the (mod 100) reciprocal of N is N+64. So the reciprocal of 33 is 97. 33*97 = 3201 = 1 (mod 100). The whole algorithm ... Suppose the tens digit of N is T. If N = 10T+1, then 1/N = 102-N 10T+3, N+64 10T+7, N+36 10T+9, 98-N Rich

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[math-fun] A power of two curiosity.
by Allan Wechsler 07 Jul '10

07 Jul '10

The 77th power of 2 is 151 115 727 451 828 646 838 272 Of the eight digit-triples that make up the number in base 10, six are palindromes. The chances of a random triplet being palindromic are 1 in 10, so I estimate the "surprisingness" of this number at about 1 in 30,000.

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Re: [math-fun] graviton-like cellular automaton
by Steve Witham 06 Jul '10

06 Jul '10

So, does a two-body system radiate away energy as gravity waves? Even if it's made of two point particles so no tidal forces? If so a simulation of a tiny (ie tractable) system with powerful gravity (to overcome the smallness) might dissipate its energy quickly.

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[math-fun] interesting numbers pages
by rcs＠xmission.com 05 Jul '10

05 Jul '10

A recent subscriber to Math-Fun, Robert Munafo <mrob27(a)gmail.com>, has some interesting Numbers pages. These are somewhat in the spirit of the Penguin Dictionary, and Lore of Large Numbers. http://mrob.com/pub/math/numbers.html http://mrob.com/pub/math/largenum.html Rich

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Re: [math-fun] graviton-like cellular automaton
by Steve Witham 05 Jul '10

05 Jul '10

>From: "George W. Hart" <george(a)georgehart.com> > > http://www.georgehart.com/Growth/growth.html Awesome. >From: James Propp <jpropp(a)cs.uml.edu> > >For an example of a CA that allows a particle moving through a universe to >modify the universe it moves through, see http://arxiv.org/abs/1002.4841 , >"Lattice gas simulations of dynamical geometry in two dimensions" by Anna >Klales, Donato Cianci, Zachary Needell, David A. Meyer, and Peter J. Love. Cool, but, "Navier-Stokes equations! Oh noes!" Which reminds me http://icanhascheezburger.files.wordpress.com/2009/06/funny-pictures-cat-up… --Steve

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[math-fun] graviton-like cellular automaton
by Mike Stay 04 Jul '10

04 Jul '10

Gravitons are presumed to change the shape of spacetime, and if there are enough of them, perhaps even its topology. Does anyone on the list know of any cellular automata that, say, change the neighborhood based on the density or topology of clumps of "on" cells, or similar? -- Mike Stay - metaweta(a)gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com

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[math-fun] Perelman refuses Clay Math Institute's million-dollar award
by Dan Asimov 03 Jul '10

03 Jul '10

<< The reclusive Russian mathematician Grigory Perelman, aka Grisha, gained worldwide fame by claiming to have solved one of the world’s most intractable mathematical problems, the Poincaré conjecture, and then disappearing in St. Petersburg. On Thursday he said he had rejected a $1 million prize from the Clay Mathematics Institute in Cambridge, Mass., for the feat. >> More at < http://www.nytimes.com/2010/07/02/science/02math.html >. --Dan I sleep as fast as possible so I can get more rest in the same amount of time.

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[math-fun] http://gosper.org/fst.pdf
by Bill Gosper 03 Jul '10

03 Jul '10

has been rewritten thanks to funster Neil Bickford spotting an error and eavesdropper Julian showing me how to restore the four illustrations (sort of). (Summary: crazy identities from, e.g., Fourier analysis of fractals). --rwg

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Re: [math-fun] Stupid antimatter questions
by Dan Asimov 02 Jul '10

02 Jul '10

Henry wrote: << How do we know whether something we're looking at in a telescope is matter or anti-matter? >> Josh wrote: << I think the main answer is that space isn't empty, and if there were a boundary between matter and antimatter anywhere we would see all the gamma rays coming from the annihilations at the boundary. >> I would add that AFAIK we have no idea what fraction of the (spatial) universe we're able to see. Usually it seems people assume it's most of the universe, or at least that the rest of it doesn't vary greatly from what we see. But what we can see could be an unimaginably small fraction of the actual universe, which might even be infinite. So, what we see may well be vastly uncharacteristic of the universe at large. --Dan I sleep as fast as possible so I can get more rest in the same amount of time.

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Re: [math-fun] Stupid antimatter questions
by Henry Baker 02 Jul '10

02 Jul '10

Tabloid journalism? We hope not -- this research is what prompted my question in the first place. But even if it is true, there should still be a lot of antimatter around in pockets of the universe, unless antimatter has some other defect -- e.g., perhaps it decays faster than matter? --- In "empty" space, one could conceivably "store" antimatter by having a ball of (neutral) matter in orbit around a ball of (neutral) antimatter of similar order-of-magnitude mass. I was wondering what the diameter of the orbit should be in order to keep the configuration from blowing up in a reasonable time scale. I'm guessing that an Earth-sized mass of matter could have a Moon-sized mass of antimatter in more-or-less circular orbit for quite a long time (mucho millions of years) -- even while giving off huge amounts of x-rays & neutrinos. Of course, we already know that the Moon, Mars, Venus & a few other bodies aren't made of antimatter, because we landed various objects on them. But what makes us so positive that all the other bodies in the Solar System are made of normal matter? At 01:13 PM 7/2/2010, Bill Gosper wrote: >Is this just tabloid journalism? >http://www.bnl.gov/bnlweb/pubaf/pr/PR_display.asp?prID=1139 >--rwg > >On Wed, Jun 30, 2010 at 11:27 AM, Henry Baker <hbaker1(a)pipeline.com ><http://gosper.org/webmail/src/compose.php?send_to=hbaker1%40pipeline.com>> >wrote:> "How do we know whether something we're looking at in a >telescope is matter or anti-matter?" > >I think the main answer is that space isn't empty, and if there were a >boundary between matter and antimatter anywhere we would see all the >gamma rays coming from the annihilations at the boundary. > >There aren't many other asymmetries! > >--Josh

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