February 2019 - mathfun@mailman.xmission.com

[math-fun] footnote re pentominoes on 8x8 with 4 holes
by Mike Beeler 15 Feb '19

15 Feb '19

These days, it's hard to know whether something is new, but a lot of web searching didn't turn up the result at the bottom here. Tiling an 8x8 with 4 cells removed, with the 12 pentominoes, is decades old. Usually the 4 are symmetric, but arbitrary placement has been discussed. If the 4 isolate 1-4 or 6 cells, tiling is obviously impossible. The one way to isolate 5 cells forces P in a corner, and has 410 solutions. There are 2 other impossible formations. One requires P in two corners. The other forces T or U in a position that isolates a cell. These are shown on the Wikipedia "pentomino" page. From the page edit trail, the second formation may have been discovered in January 2007 ("found another unsolvable"). I confirm these are the only non-isolating, impossible formations. Now for the maybe new thing. For the many other configurations of the 4 holes, what is the minimum number of solutions, and what configurations have that minimum? The minimum is 12 solutions, and only one pattern has 12 solutions: - - - - - - - - - - - - - - - - - - - - - - - - X - - - - - - - - X - - - - - - - - - - - - - - - - X - - - - - - - - X - - - - -- Mike Beeler

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Re: [math-fun] bosebola?
by Bill Gosper 13 Feb '19

13 Feb '19

On 2019-02-11 11:07, Veit Elser wrote: > If you uniformly sample from the partitions of an integer N, and > interpret the sequence of parts, sorted largest to smallest, as a > (decreasing) function y(x), then in the limit of large N the y(x) of > the “typical" partition satisfies (after rescaling) > > (e^x-1)(e^y-1) = 1 Providing a somewhat unlikely looking involution: Out[755]= Function[x, x - Log[-1 + E^x]] In[760]:= NestList[%755, a, 9] // FullSimplify; In[761]:= Assuming[a > 0, FullSimplify@%] Out[761]= {a, a - Log[-1 + E^a], a, a - Log[-1 + E^a], a, a - Log[-1 + E^a], a, a - Log[-1 + E^a], a, a - Log[-1 + E^a]} (Also works for a:=±i, i+1, etc., but not -1.) > > Does this curve have a name? > Hyperbolic hyperbola? HyperPERbola for short. Perhybola? > -Veit >

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[math-fun] HAKMEM Munching Squares bug report!
by Henry Baker 12 Feb '19

12 Feb '19

I'm still getting bug reports for code that runs on hardware that no longer exists! "I believe HAKMEM Item 146: Munching Squares has a bug. I tried the code on a PDP-10 and 340 display emulator, but it wouldn't work. I compared against the PDP-1 version and found a difference. I think the XOR 1,2 instruction should be XOR 2,1."

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[math-fun] Recommending Geoffrey Campbell
by David Wilson 12 Feb '19

12 Feb '19

I would like to recommend Geoffrey Campbell to the math-fun mailing list. His Facebook profile is here: https://www.facebook.com/geoffrey.campbell.180 He says he has attempted to subscribe via https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun but "It kept declining my email address and proposed password - the entry requirement." At any rate, Geoffrey regularly posts some interesting math puzzlers on LinkedIn Number Theory group, which is how I encountered him. I think he would make a good member, if there are no objections.

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[math-fun] bosebola?
by Veit Elser 12 Feb '19

12 Feb '19

If you uniformly sample from the partitions of an integer N, and interpret the sequence of parts, sorted largest to smallest, as a (decreasing) function y(x), then in the limit of large N the y(x) of the “typical" partition satisfies (after rescaling) (e^x-1)(e^y-1) = 1 Does this curve have a name? -Veit

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Re: [math-fun] bosebola?
by Dan Asimov 12 Feb '19

12 Feb '19

I've seen something like it where the asymptotes are some other two intersecting lines ax + by = c in the plane. (It's probably the result of applying a linear mapping to the curve (e^x-1)(e^y)-1 = 1). It was used in a relatively recent proof that zeta(2) = π^2/6, based on (I think) integrating to get the area bounded by such curves and straight lines. Sorry I don't have the specifics. —Dan ----- Right. You can get the numerical factor by finding the area under the curve. Nobody has seen this curve before? -----

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[math-fun] Draft of February 2019 blog post
by James Propp 12 Feb '19

12 Feb '19

I'm soliciting comments and suggestions for my February "Mathematical Enchantments" essay (http://mathenchant.org/045-draft2.pdf) especially comments of a mathematical or historical nature, but also comments of a stylistic nature (I'm always looking for ways to improve my prose). And my essays tend to be too long, so if you see a passage that you think should be cut (or relegated to an Endnote), please let me know. I'll post my essay at my WordPress site early on the 17th of the month (or late on the 16th), but I can continue to make changes indefinitely, so comments are welcome at any time. Thanks, Jim Propp

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[math-fun] Q: Where do we get mercury?
by Bill Gosper 11 Feb '19

11 Feb '19

A: H. G. Wells. When I was a kid, at least two friends had a bottle of Hg in their garage. I don't know why. We often played with it, smearing it on pennies, e.g.. If we spilled it, we could sweep it up and put it back in the bottle. I had numerous medical relatives who kept lots of mercurochrome and merthiolate. (AKA the infamous autismogenic thimerosal.) And we all had amalgam fillings. Rich and Hilarie named their daughter Mercury! "Almaden" is still a popular place|business name around San Jose, where the natives used cinnabar for warpaint. And the paper is still Mercury News. DHS might be interested in people trying to make the fulminate, but *much* more interested in the terror potential of the nightmarish compound methyl mercury, from which even a hazmat suit might not protect you from slow, agonizing braindeath. Fear of spontaneous formation of methyl mercury probably fuels today's mercury hysteria. —rwg When bottom-feeders ingest too much mercury, they can't get off the bottom. On 2019-02-09 13:40, Henry Baker wrote: > Thanks, Hilarie! > > I never read that story when I was a kid. > > I presume that someone actually built such a "mercuryball" at the time > to test it out? > > I also presume that playing with such a ball today would cause DHS > instant apoplexy. Someone brought liquid mercury to one of the high > schools in L.A. a few years ago, and the officials evacuated the > school and brought in people in hazmat suits to remove any possible > mercury spills. Irony alert: they apparently didn't realize that a > much bigger mercury poisoning threat existed within every fluorescent > bulb in the school. > > The problem with a mercuryball is that it isn't "smart" or self-powered. > > At 10:48 PM 2/8/2019, Hilarie Orman wrote: >>Cf. "Stand By For Mars", Tom Corbett, Space Cadet, and the game >>of mercury ball. >> >>> If the ball were flying through the air, it >>> could set up asymmetric drag and change its >>> trajectory to some degree. Even if it weren't >>> *guided*, it could still move in a random and >>> impossible-to-predict manner which would >>> thoroughly confuse even the best goalies. >> >>Hilarie >>lman.xmission.com/cgi-bin/mailman/listinfo/math-fun >

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Re: [math-fun] math-fun Digest, Vol 192, Issue 9
by Stuart Anderson 11 Feb '19

11 Feb '19

The problem with a mercuryball is that it isn't "smart" or self-powered. Animals are smart and self-powered, but generally they aren't round. But what if they were? https://m.facebook.com/story.php?story_fbid=10156997246687008&id=1137038220… On Mon, Feb 11, 2019, 06:00 <math-fun-request(a)mailman.xmission.com wrote: > Send math-fun mailing list submissions to > math-fun(a)mailman.xmission.com > > To subscribe or unsubscribe via the World Wide Web, visit > https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun > or, via email, send a message with subject or body 'help' to > math-fun-request(a)mailman.xmission.com > > You can reach the person managing the list at > math-fun-owner(a)mailman.xmission.com > > When replying, please edit your Subject line so it is more specific > than "Re: Contents of math-fun digest..." > > > Today's Topics: > > 1. Re: "Smart" soccer balls ? (Henry Baker) > > > ---------------------------------------------------------------------- > > Message: 1 > Date: Sat, 09 Feb 2019 13:40:18 -0800 > From: Henry Baker <hbaker1(a)pipeline.com> > To: Hilarie Orman <ho(a)alum.mit.edu>,math-fun > <math-fun(a)mailman.xmission.com> > Subject: Re: [math-fun] "Smart" soccer balls ? > Message-ID: <E1gsaNH-000Dux-MV(a)elasmtp-masked.atl.sa.earthlink.net> > Content-Type: text/plain; charset="us-ascii" > > Thanks, Hilarie! > > I never read that story when I was a kid. > > I presume that someone actually built such a "mercuryball" at the time to > test it out? > > I also presume that playing with such a ball today would cause DHS instant > apoplexy. Someone brought liquid mercury to one of the high schools in > L.A. a few years ago, and the officials evacuated the school and brought in > people in hazmat suits to remove any possible mercury spills. Irony alert: > they apparently didn't realize that a much bigger mercury poisoning threat > existed within every fluorescent bulb in the school. > > The problem with a mercuryball is that it isn't "smart" or self-powered. > > At 10:48 PM 2/8/2019, Hilarie Orman wrote: > >Cf. "Stand By For Mars", Tom Corbett, Space Cadet, and the game > >of mercury ball. > > > >> If the ball were flying through the air, it > >> could set up asymmetric drag and change its > >> trajectory to some degree. Even if it weren't > >> *guided*, it could still move in a random and > >> impossible-to-predict manner which would > >> thoroughly confuse even the best goalies. > > > >Hilarie > >lman.xmission.com/cgi-bin/mailman/listinfo/math-fun > > > > > ------------------------------ > > Subject: Digest Footer > > _______________________________________________ > math-fun mailing list > math-fun(a)mailman.xmission.com > https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun > > > ------------------------------ > > End of math-fun Digest, Vol 192, Issue 9 > **************************************** >

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Re: [math-fun] "Smart" soccer balls ?
by Hilarie Orman 09 Feb '19

09 Feb '19

Cf. "Stand By For Mars", Tom Corbett, Space Cadet, and the game of mercury ball. > If the ball were flying through the air, it > could set up asymmetric drag and change its > trajectory to some degree. Even if it weren't > *guided*, it could still move in a random and > impossible-to-predict manner which would > thoroughly confuse even the best goalies. Hilarie

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