December 2014 - mathfun@mailman.xmission.com

[math-fun] record of factoring
by Simon Plouffe 03 Dec '14

03 Dec '14

hello, they could factor a 5 digit number 233 x 241 = 56153 using a quantum computer. // http://science.slashdot.org/story/14/12/03/1551239/mathematical-trick-helps… this is impressive, well, sort of. best regards, Simon Plouffe

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[math-fun] music theory
by Warren D Smith 03 Dec '14

03 Dec '14

https://dl.dropboxusercontent.com/u/3507527/MusicTh.html explains "Warren Smith's theory of music." The claim is that music is a debugging tool. It also contains some analysis about tuning, frequencies, musical scale, which you've recently been talking about. The fact the traditional western scale has 12 notes seems not to be a coincidence; it is best possible. See "Why the 12-note scale?" within it. -- Warren D. Smith http://RangeVoting.org <-- add your endorsement (by clicking "endorse" as 1st step)

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[math-fun] 1. Re: The Saddest Thing about the Integers
by Stuart Anderson 03 Dec '14

03 Dec '14

It's an interesting exercise to look for equal divisions of the octave into n intervals that provide bettter approximations to (say) 3rd, 5th, 7th harmonics than n = 12 . WFL Continued fractions is one way to get better approximations. I think there is also a method that uses the Stern-Brocot tree but I can't find a reference. Heres some links on scales and continued fractions; http://www.math.uwaterloo.ca/~mrubinst/tuning/12.html http://www.math.niu.edu/~rusin/uses-math/music/12 Stuart Anderson

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[math-fun] More sad integers
by James Propp 03 Dec '14

03 Dec '14

Those who enjoy Diophantine approximation questions like these might also enjoy thinking about why the Fibonacci numbers 13,21,34,55,89 have the same initial digits as the Fibonacci numbers 1,2,3,5,8. It makes for a pleasant bit of napkin-math. Jim Propp

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Re: [math-fun] Geek Sublime
by Hilarie Orman 03 Dec '14

03 Dec '14

Oddly enough, someone who was more interested in the Sanskrit than the programming recommended this book to me recently. Despite the mixed reviews, I bought it and have skimmed through it. It seems long-winded and meandering, but interesting. I had no idea that Sanskrit had such a long history of formal grammar. In high school, I was inspired to give a lecture to my second year Latin class about generating sentences through rules. The concept was marred by my ignorance of formal grammar, computers, any other language except English, etc. But, I always wondered if the logic of Latin shaped my interest in mathematics and computers, or if I was already such a hopeless geek by that time that I was unable to absorb a language in other way than algorithmically. And why should that be? I don't think the book answers my question, but it may cause pleasing mind wandering. Hilarie > From: Dan Asimov <dasimov(a)earthlink.net> > Date: Tue, 2 Dec 2014 11:21:48 -0800 > Subject: [math-fun] Geek Sublime > This book, "Geek Sublime" by Vikram Chandra, looks interesting: > < http://www.amazon.com/Geek-Sublime-Vikram-Chandra/dp/0571310303/ >. > Has anyone read it? > --Dan

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[math-fun] Counterflow (Any kids on math-fun?)
by Bill Gosper 01 Dec '14

01 Dec '14

gosper.org/counterflow.pdf is a (hopefully) pleasant little problem + spoiler. --rwg

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[math-fun] Black Hole Binaries can eject relativistic normal stars
by Henry Baker 01 Dec '14

01 Dec '14

FYI -- Apparently, just like planets & planetoids can be ejected from solar systems, regular stars can be ejected from a system of binary black holes. I presume that "living" in a planetary system of such a star would provide time dilation relative to the rest of the universe. Of course, the event which accelerated the star in the first place might a) strip the star of all/most of its planets; or at least b) kill all life on any such planets that do manage to escape with the star. http://arxiv.org/abs/1411.5030 Observational Cosmology With Semi-Relativistic Stars Abraham Loeb (1), James Guillochon (1) ((1) Harvard ITC) (Submitted on 18 Nov 2014) "Galaxy mergers lead to the formation of massive black hole binaries which can accelerate background stars close to the speed of light. We estimate the comoving density of ejected stars with a peculiar velocity in excess of $0.1c$ or $0.5c$ to be $\sim 10^{10}$ and $10^5$ Gpc$^{-3}$ respectively, in the present-day Universe. Semi-relativistic giant stars will be detectable with forthcoming telescopes out to a distance of a few Mpc, where their proper motion, radial velocity, and age, can be spectroscopically measured. In difference from traditional cosmological messengers, such as photons, neutrinos, or cosmic-rays, these stars shine and so their trajectories need not be directed at the observer for them to be detected. Tracing the stars to their parent galaxies as a function of speed and age will provide a novel test of the equivalence principle and the standard cosmological parameters. Semi-relativistic stars could also flag black hole binaries as gravitational wave sources for the future eLISA observatory." "In the context of astro-biology, SHS could spread life beyond the boundaries of their host galaxies [26, 27]."

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[math-fun] combining statistical significances
by Warren D Smith 01 Dec '14

01 Dec '14

http://rangevoting.org/CombinedTestFail.html now manages to come out the other end of the amazing combinatorics to devise simple algorithm. Unfortunately my understanding of this problem is still not as good as one would like.

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[math-fun] The lissajoke rolling on Bob Hearn's floor plus Euler disk breakthrough
by Bill Gosper 01 Dec '14

01 Dec '14

Thane>I took a video of a metal version of Bill Gosper's lissajoke rolling on the floor at Bob Hearn's house ( http://gosper.org/lissajoke.gif ). Completely coincidentally, Bob Hearn is narrating its ambiguous rolling behavior as I'm pushing it around on the floor. Anyway, here is the videohttps://www.youtube.com/watch?v=7YpYCgRt9Qc&list=UUbBGpH5hVMFF23WjuaFz… The ambiguous rolling effect is quite noticeable when I push it farther away. ------------- rwg>Alan Adler's rejoinder suggests rpm outweighs viewing distance. And mentions something much more newsworthy: AJA>I posted the Lissajous video here http://youtu.be/Rli5x91Jg64 with this description: This is a rotating Lissajous shape designed by mathematician Bill Gosper. The shape is four inches in diameter and is rotating about its axis. Guess the orientation of the axis (either horizontal or vertical). There's a good chance that you'll guess wrong. There is another Gosper Lissajous shape here https://www.youtube.com/watch?v=7YpYCgRt9Qc I posted my 5:54 Euler disc run herehttp://youtu.be/N_bMbuEQ6wM <AJA Joe Kisenwether suggested building the object that actually does what https://www.youtube.com/watch?v=LGUfgplJRSc seems to do. NeilB figured out what he meant, and Meshlabbed it for Shapeways. Unfortunately, UPS delivered it smashed (but in an unsmashed box). Neil's dad pretty well straightened the thing with his bare hands, and on the Thanksgiving dinner table, just before we ate, Neil shot https://www.youtube.com/watch?v=M16IuOioz1k (Roller machine by Alan Adler.) --rwg

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