August 2018 - mathfun@mailman.xmission.com

[math-fun] I just saw CA plate XKCD793.
by Bill Gosper 05 Aug '18

05 Aug '18

Puzzle: It was orange on black. Seven letter vanities ("environmentals") were not introduced until decades after the switch to orange on blue. I distinctly remember an episode of Columbo where the perp had orange on blue CARSINI, a safe bet for the writers, before seven letters were legal. --rwg If I see XKCD1047, I'll know it's a fake. (Note the rollover warning about πᵗʰ root.) WRI support just told me the secret way to get Mma to display πᵗʰ root of 4. (http://www.tweedledum.com/rwg/idents.htm)

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Re: [math-fun] I just saw CA plate XKCD793.
by Dan Asimov 04 Aug '18

04 Aug '18

Bill Gosper wrote: ----- ..... ..... (http://www.tweedledum.com/rwg/idents.htm) ----- Ramanujan lives on! —Dan

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[math-fun] Simplest planar n-gon polyhedra
by Ed Pegg Jr 04 Aug '18

04 Aug '18

At https://math.stackexchange.com/questions/2869725/ I've started a sequence. What is the fewest number of planar but possibly irregular n-gons needed to make a polyhedron or toroid? 4 triangles 6 squares 12 pentagons 7 hexagons 12 heptagons Correct so far? How many octagons are needed? Ed Pegg Jr

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Re: [math-fun] N-athlon proposal and the Rain Man
by Dan Asimov 03 Aug '18

03 Aug '18

I have a different take. I think most of us could beat the chimp if we had enough practice. Probably playing the game daily for a month should be more than enough. Oh, yeah, and especially if we got something we really wanted each time we got it right. —Dan Tom Kazes wrote: >Hah, I thought of that exact same clip! That chimp is amazing. >Even if the numbers were displayed the entire time, I doubt I >could match its speed. I wonder if orangutans and gorillas >have the same ability? >Brent Meeker writes: > > Or there could be a game that required you to quickly recognize and > > remember the numbered order of squares on a screen. > > > > https://www.npr.org/sections/krulwich/2014/04/16/302943533/the-ultimate-ani… > > > > Or maybe not. > > > > Brent > > > > On 8/2/2018 7:33 PM, Dan Asimov wrote: > > > I've been thinking it might be fun to have a computer graphics game > > > that challenges you to guess the number of items on the screen quickly. > > > > > > With feedback, I wonder how proficient one can become at that. Say they > > > are all just circular dots. > > > > > > Likewise there could be a program challenging you to guess the ratio of lengths of two curves or areas of two shapes on the screen. > > > > > > —Dan > > > > > > > > > Rich Schroeppel wrote: > > > ----- > > > A splatter of even 25 toothpicks is likely to contain ambiguities, where, > > > because of overlaps, the image is insufficient to distinguish each toothpick. > > > ----- > > > > >_______________________________________________ >math-fun mailing list >math-fun(a)mailman.xmission.com >https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun

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Re: [math-fun] N-athlon proposal and the Rain Man
by Dan Asimov 03 Aug '18

03 Aug '18

For me, attempting feats of memory doesn't appeal, for some reason, but attempting feats of estimation does. —Dan Brent Meeker wrote: >Or there could be a game that required you to quickly recognize and >remember the numbered order of squares on a screen. > >https://www.npr.org/sections/krulwich/2014/04/16/302943533/the-ultimate-ani… > >Or maybe not. > >Brent > >On 8/2/2018 7:33 PM, Dan Asimov wrote: >> I've been thinking it might be fun to have a computer graphics game >> that challenges you to guess the number of items on the screen quickly. >> >> With feedback, I wonder how proficient one can become at that. Say they >> are all just circular dots. >> >> Likewise there could be a program challenging you to guess the ratio of lengths of two curves or areas of two shapes on the screen. >> >> —Dan >> >> >> Rich Schroeppel wrote: >> ----- >> A splatter of even 25 toothpicks is likely to contain ambiguities, where, >> because of overlaps, the image is insufficient to distinguish each toothpick. >> ----- >> >> _______________________________________________ >> math-fun mailing list >> math-fun(a)mailman.xmission.com >> https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun > > >_______________________________________________ >math-fun mailing list >math-fun(a)mailman.xmission.com >https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun

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Re: [math-fun] N-athlon proposal and the Rain Man
by Dan Asimov 03 Aug '18

03 Aug '18

I've been thinking it might be fun to have a computer graphics game that challenges you to guess the number of items on the screen quickly. With feedback, I wonder how proficient one can become at that. Say they are all just circular dots. Likewise there could be a program challenging you to guess the ratio of lengths of two curves or areas of two shapes on the screen. —Dan Rich Schroeppel wrote: ----- A splatter of even 25 toothpicks is likely to contain ambiguities, where, because of overlaps, the image is insufficient to distinguish each toothpick. -----

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[math-fun] N-athlon proposal and the Rain Man
by Veit Elser 03 Aug '18

03 Aug '18

I’ve been absent from math-fun for a while, but from a quick glance at recent posts I see mention of N-athlons and visual estimation of shapes. Strangely, these combine in a new, untested, race that involves parked cars. The idea is to have the runners shout out the N-fold symmetry of the parked car hubcaps as they are passing them. You’d have to space the runners, so they cannot hear each other. But I think you get the idea: to get a good time you can’t afford to stop and count spokes (or whatever) to determine N. For example, you can train your eye/brain to determine if there is a line of bilateral symmetry, and then the existence or non-existence of an equivalent line orthogonal to that. Now you are dealing with N congruent to 0 or 2 mod 4, and for N not too large (<20) the ball-park-estimate part of your brain should be able to quickly arrive at say, 18 (don’t ask me why, but they exist). In the movie Rain Man, the title character was able to count objects almost instantaneously, up to the hundreds. Such people would do very well in my proposed race, and without clever tricks … or so you would think. Although it’s been a long time since I saw that movie, I clearly recall that when he was counting the number of spilled matches on the floor he verbalized 62,62,62,62 … 248 (please correct me if I got the numbers wrong). So it seems the Rain Man was able to directly see the factorization! Alternative hypothesis: he really liked 62 as a unit, and it was a lucky accident that it came out even. -Veit

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[math-fun] Fields medalists
by Bernie Cosell 02 Aug '18

02 Aug '18

<https://www.nytimes.com/2018/08/01/science/fields-medals-mathematics.html> /B\ Bernie Cosell bernie(a)fantasyfarm.com -- Too many people; too few sheep --

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Re: [math-fun] On a clear day at Battersea power station
by Bill Gosper 02 Aug '18

02 Aug '18

Fred: Pls email me these pix and I'll host them. --rwg I cannot refrain from adding: Screw DropBox. << Scale diagrams of these solutions might be appreciated here ...? >> Quite so. In a pleasant inversion of the scholastic dictum that a diagram does not constitute a proof, a clutch of accurate diagrams immediately discloses that: The obvious interpretation of a signed sightline distance --- that the correct angle is made only with a line segment directed _away_ from the tower --- was after all perfectly correct. Hence --- assuming an observer lacking eyes in the back of the head --- my second and fourth solutions were duds, and only the other two remain standing (outside the rectangle). Corrected summary & diagrams, and program & results, are posted at https://www.dropbox.com/s/gva6w9ni9y6svp1/battersea.pdf https://www.dropbox.com/s/175plix3vkvxqoj/battersea_run.txt This has turned out to be an unexpectedly involved exercise: in particular, a neat elementary application of Gröbner bases, as well as an excellent topic for an undergraduate project; perhaps in a situation calling for an especially --- ahem --- challenging one ... Fred Lunnon

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[math-fun] When is base 2 not binary?
by Bill Gosper 01 Aug '18

01 Aug '18

When the digits are 0 and 1 and the other two cuberoots of 1. See gosper.org/gaskettalk.pdf pp 11 and 13. E.g., i/√3 = red.cyangreencyangreencyangreen... = cyan.greenmagentagreenmagentagreen... . Presumably we can expect a lot of these multiple representations when the unit patch has a fractal boundary. PUZZLE: Here of dimension what? We need |base|² digits to cover a positive area in the complex plane. The "France fractal" bounds the unit patch of the base 2+i^(2/3) with digits zero and the 6th roots of 1. |2+i^(2/3)| = √7. Base 2+i^(2/3) with three digits moved outward gosper.org/base2+w.bmp has a unit patch with a boundary of large dimension. (PUZZLE: D=?) --rwg

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