September 2014 - mathfun@mailman.xmission.com

Re: [math-fun] "Steampunk" mathematics?
by Dave Dyer 12 Sep '14

12 Sep '14

And how could I neglect both the Enigma machines and Turing's "bombe" devices, which were mechanical computers used to codebreak enigma messages.

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[math-fun] Bill Tutte Memorial
by Stuart Anderson 12 Sep '14

12 Sep '14

A memorial to William T Tutte has been unveiled, focussing on his cryptographic work in WWII. There is also a reference to squared squares but no attempt to cover his other mathematical discoveries in combinatorics and graph theory. http://www.tnmoc.org/news/notes-museum/bill-tutte-memorial-unveiled

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Re: [math-fun] "Steampunk" mathematics?
by Henry Baker 11 Sep '14

11 Sep '14

Very cool! I'd say that this one was within reach of Archimedes himself. BTW, it occurred to me that the "Steampunk" alternative universe is a very interesting theory. You could just tell that the Victorians were itching to do some serious calculations, both numerical & algebraic. Perhaps 100 years were wasted on "trivial" and/or "linear" models of things, because we didn't have computers to calculate anything better. An awful lot of engineers during that 100 years were stuck doing far-less-than-optimal designs, because they had no good design tools to work with. Just go back & read some of the engineering textbooks of the 1940's and 1950's. It's heartbreaking, in retrospect. Perhaps if some 19th Century American business tycoon had decided that a Babbage Engine was just the ticket to world domination... At 05:53 PM 9/11/2014, Victor Miller wrote: >There's Lehmer's bicycle sieve: http://en.wikipedia.org/wiki/Lehmer_sieve > >Victor

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Re: [math-fun] "Steampunk" mathematics?
by Henry Baker 11 Sep '14

11 Sep '14

That's Charles Bennett's whole point about reversible computers; all the work goes into resetting them! ;-) Thanks very much for the links. I've contacted Dewdney to try to get a copy of his binary elephants computer piece. At 05:33 PM 9/11/2014, Jeff Caldwell wrote: >A billiard-ball computer was on display in the lobby of MIT's Stata >Center a couple of weeks ago. It was fun to run it once, but we didn't >have time to learn to reset it.

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[math-fun] Cut, flip, replace, repeat
by James Propp 11 Sep '14

11 Sep '14

In the September 2014 issue of Math Horizons (page 8), Stan Wagon poses the following problem, which he says originated as a problem in the 1968 Moscow Mathematical Olympiad: A round cake has icing only on top. Cut out a piece in the usual shape (a sector of the circle), turn it upside down, and replace it to restore roundness. Repeat with the next piece; that is, move counterclockwise, cut out a piece with the same central angle, flip it, and replace it. Continue this process. If a piece has a knife cut from a previous iteration, ignore the cut and flip the piece as if it was solid. For pieces with 45 degree central angles, it takes 16 flips to return all icing to the top of the cake; if 180 degrees is used, it takes only four flips. How many flips does it take when the central angle is 181 degrees? Pete Winkler poses a similar problem in Mathematical Mind-Benders, which he says "was passed to me by French graduate student Thierry Mora, who heard it from his prep-school teacher Thomas Laorgue" (who didn't invent the problem and didn't know its origin). Does anyone have access to the 1968 Moscow Olympiad problems? If so, can he/she provide an English translation of the original problem? I'd be especially interested in knowing who is credited with inventing the problem (though often this kind of information is hard to dig up). Jim Propp

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[math-fun] Sweet Aha!
by Bill Gosper 11 Sep '14

11 Sep '14

By mere inspection, six green snowflakes surround a larger white one which has how many times a <http://gosper.org/kokoch.pdf> green one's <http://gosper.org/kokoch.pdf> area? <http://gosper.org/kokoch.pdf> gosper.org/kokoch.pdf --rwg (Note Julian's tool, even for a lowly Snowflake.)

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[math-fun] in the 70s that old XGP also made
by Bill Gosper 11 Sep '14

11 Sep '14

gosper.org/fracfractal.png (to lower order). It sort of has two levels of fractalness. Variations beckon. Some of which may have sweet implementations using Julian's recursivefractal magic . --rwg

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[math-fun] speed of our galaxy
by Warren D Smith 09 Sep '14

09 Sep '14

First of all, there IS a preferred rest frame, the CMB frame. If you are in that frame, the CMB (cosmic microwave background radiation) is uniform in all directions. If you are in any other frame, then the CMB is doppler shifted and looks bluer in the direction you are moving, and redder in other direction. From http://en.wikipedia.org/wiki/Cosmic_microwave_background#CMBR_dipole_anisot… : "From the CMB data it is seen that our local group of galaxies (the galactic cluster that includes the Solar System's Milky Way Galaxy) appears to be moving at 369+-0.9 km/s relative to the reference frame of the CMB" From http://en.wikipedia.org/wiki/Milky_Way : it claims milky way is moving at 552 km/sec versus CMB. http://en.wikipedia.org/wiki/Andromeda_Galaxy Milky Way & Andromeda are approaching each other at about 140 km/sec and will collide. This all is a very small speed compared to c = 299792 km/sec. Our speed is less than 0.002 c. Also note, the escape velocity from our galaxy from here, is about 500 km/sec, (larger if wanted to escape from the core) so these speeds are of the same order as you would naively expect for gravitational reasons, and the virial theorem. What is the source of all these speeds? Ultimately, it comes from fluctuations in the early universe. These small fluctuations can still be seen in the CMB sky maps produced by WMAP and planck satellite. In a perfectly uniform universe there would be no speed and density fluctuations. These initial fluctuations self-amplified via gravitational effects. What actually seems much more surprising to me is the existence of vast "jets" moving at relativistic speeds, thought to be ejected from black holes as a side effect of infall and relativistic magneto-hydrodynamics somehow.

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[math-fun] speed of our galaxy : 630 km per second but how can this be possible ?
by Simon Plouffe 09 Sep '14

09 Sep '14

Hello, A very interesting news came out these days about a group of astrophysicists found a way to make a path of direction of many known galaxies in the area. By area I mean a large cube of 500 million light years wide called Laniakea which has nothing to do with Ikea. They used intense calculations, (HÃ©lÃ¨ne Courtois), http://www.francetvinfo.fr/sciences/espace/qu-est-ce-que-laniakea-le-superc… The result is astonishing and the word is weak, it is mind blowing in my opinion. See the short film (in french). So according to those calculations, one thing we already knew is that our own galaxy is travelling at a speed of 630 km per second, this is impressive if we consider the mass of the galaxy, it takes 476 years to travel 1 light year and since the beginning of the known birth of earth, we travelled about 10 million light years. BUT : there is a simple question : how can this be possible if we consider the pure energy to accelerate such an astronomic mass (the weight of the galaxy), and in more general terms : how can such a mass can acquire any speed at all ?? Can anyone has an explanation for this ? best regards, Simon Plouffe

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Re: [math-fun] antiprism oddity
by Bill Gosper 06 Sep '14

06 Sep '14

Thane>hmmm—who would be the right person to create this prank animation? On Fri, Sep 5, 2014 at 9:49 PM, Bill Gosper <billgosper(a)gmail.com> wrote: Twist "top" face half a "click" wrt to its opponent. This makes an ordinary prism with rectangular faces diagonally slashed. If you twist a whole click the other way, the whole figure will mirror-image. I.e., the slashes flip to the opposite diagonal. You could make a prank animation of the top face continuously rotating wrt the bottom, by repeatedly fading out the slash and fading up its mirror image, or have both slashes present at the "prism points". --rwg gosper.org/twist.gif I can't believe I wasted an hour on this. --rwg

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