May 2019 - mathfun@mailman.xmission.com

Re: [math-fun] bad influence
by Dave Dyer 14 May '19

14 May '19

insert here the old thread about the dangerous group Al'gebra

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[math-fun] The irrational 10-adic idempotents
by James Propp 14 May '19

14 May '19

Has anyone studied the distribution of the digits of the 10-adic idempotents ...890625 and ...109376? See sequences A018247 and A018248 in the OEIS. The governing recurrences might be tractable (or at least more tractable than the recurrences governing the digits of p-adic quadratic irrationals). Jim Propp

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Re: [math-fun] US Opposition to teaching of Arabic Numerals at 56%
by Dan Asimov 14 May '19

14 May '19

I think we can read this into it: A heckuva lot of people feel free to express opinions about subjects they don't know enough about to express an opinion about. —Dan Allan Wechsler wrote: ----- Don't think we can read too much into this. It's simple, understandable ignorance of a piece of technical vocabulary. -----

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[math-fun] Intersection of random cosets of Z[exp(2πi/3)]: When is this set empty?
by Dan Asimov 14 May '19

14 May '19

Let E denote the triangular lattice Z[w] of Eisenstein integers, where w = -1/2 + i sqrt(3/4) is a primitive 1^(1/3) in C. For j = 1, 2, ...,n let A_j = K_j + L_j w ≠ 0 and B_j = M_j + N_j w be arbitrary elements of E with all A_j nonzero. Multiplication by A_j carries E into a subset of itself by uniform scaling, and translation by B_j carries E onto itself isometrically. Thus for each j, 1 <= j <= n, the set X_j = A_j E + B_j = {A_j u + B_j | u in E} is a subset of E isometric to a uniformly scaled copy of itself. Question: --------- Find an algorithm in terms of the A_j and B_j that determines whether or not the sets X_1, ..., X_n have nonempty intersection. —Dan

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Re: [math-fun] The Doormat Singers at MIT
by Bill Gosper 12 May '19

12 May '19

I believe that was written by PDP-1 Teco creator and WTBS DJ Dan Murphy, for performance in the annual All Tech Sing, or whatever they called it. (Wherein the "co-eds" substituted "Kenneth R. Wadleigh" for "Officer Krupke".) Big Julie was President Julius Adams Stratton, after a TV skit about Julius Caesar. (Stratton was the guy for whom Bill Ackermann rented a tux, just so he could say, "It certainly is a pleasure!".) —rwg I should have added in my Stirling post that the errors are monotone decreasing (= "antitone"). On Sun, May 12, 2019 at 2:02 PM rwg <rwg(a)ma.sdf.org> wrote: > > > -------- Original Message -------- > Subject: Re: [math-fun] The Doormat Singers at MIT > Date: 2019-05-12 13:40 > From: Dan Asimov <dasimov(a)earthlink.net> > To: math-fun <math-fun(a)mailman.xmission.com> > Reply-To: Dan Asimov <dasimov(a)earthlink.net>, math-fun > <math-fun(a)mailman.xmission.com> > > Hans! Thanks for a wonderful blast from the past — about 54 years ago. > > The mp3 was better than any lyrics! > > —Dan > > > > DA: "Can anyone recall the lyrics, or know where they can be found, to > > a song from '64-'65 that had words like: As I walked out, one May > > morning, along the shady route, ..." > > > > Look for "The Institute Screw" here: > > > > http://www.dpbsmith.com/doormat/ > > > > No lyrics but they have an mp3. > > _______________________________________________ > 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] The Doormat Singers at MIT
by Dan Asimov 12 May '19

12 May '19

Hans! Thanks for a wonderful blast from the past — about 54 years ago. The mp3 was better than any lyrics! —Dan >DA: "Can anyone recall the lyrics, or know where they can be found, to a song from '64-'65 that had words like: As I walked out, one May morning, along the shady route, ..." > >Look for "The Institute Screw" here: > >http://www.dpbsmith.com/doormat/ > >No lyrics but they have an mp3.

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Re: [math-fun] Stirlingoid figure of merit
by Dan Asimov 12 May '19

12 May '19

Can anyone recall the lyrics, or know where they can be found, to a song from '64-'65 that had words like: ----- As I walked out, one May morning, along the shady route, There I met Big Julie, the keeper of the 'Tute. I said to him, "Big Julie, how are your students all?" He said to me every one of them is screwed right to the wall! ----- I had no luck trying to google this. —Dan

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Re: [math-fun] Draft of my May 17, 2019 essay
by Dan Asimov 12 May '19

12 May '19

I regret that I cannot concur with my esteemed colleague on this matter: I don't think it's an great idea to begin a title with the word "But". Intoxication by alcohol alone is not necessarily sufficient to achieve Buddha-wisdom! —Dan Adam Goucher wrote: ----- The latter, definitely: it flows better to have the quote as the title, and the description as the subtitle. (As I happened to drink wine this evening, to a non-trivial extent, I claim to be in a position to judge* matters pertaining to both mathematicians and intoxication.) * no pun intended. -----

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[math-fun] When in doubt, use 0, 1, or take the square root.
by Ed Pegg Jr 11 May '19

11 May '19

Square or take the square root. In my Substitution Tilings program at http://demonstrations.wolfram.com/SubstitutionTilings/ , I have a routine called SqrtSpace. Pictures at https://community.wolfram.com/groups/-/m/t/1679969 In the Psi Quad tiling, https://community.wolfram.com//c/portal/getImageAttachment?filename=PsiQuad… , the algebraic number field is Psi, ψ, the https://en.wikipedia.org/wiki/Supergolden_ratio . The coordinates in the tiling are NOT in the algebraic number field of ψ, since sextics are involved. However, with a sign-preserving squaring or square root operation, all coordinates work perfectly within the algebraic number field. I expand on this more at https://blog.wolfram.com/2019/03/07/shattering-the-plane-with-twelve-new-su… Squaring/sqrt makes coordinates elegant for extremal orchard solutions. https://blog.wolfram.com/2018/02/02/cultivating-new-solutions-for-the-orcha… Squaring makes all vertices elegant for degenerate power simplex coordinates. http://demonstrations.wolfram.com/DegeneratePowerSimplices/ "If it doesn't work, try squaring your values." -- I've heard this since college, but I didn't expect it to work so well in algebraic number fields. Is there a name for this? Ed Pegg Jr

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[math-fun] Draft of my May 17, 2019 essay
by James Propp 11 May '19

11 May '19

I've written another essay (a little shorter than usual), which I'll either call A Mathematician in the Jury Box, or, “But how should we define ‘intoxicated’?” or “But how should we define ‘intoxicated’?”, or, A Mathematician in the Jury Box (I can't decide which is better). See http://mathenchant.org/048-draft2.pdf Comments are welcome! Jim

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