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[math-fun] Tetrahedral hypercube projection
by James Propp 14 May '18

14 May '18

Let u, v, w, and x be the vectors from the center of a tetrahedron to the four vertices. Does the zonohedron formed by the fifteen vectors u, v, w, x, u+v, u+w, u+x, v+w, v+x, w+x, u+v+w, u+v+x, u+w+x, v+w+x, and u+v+w+x=0 have a name? Better, are there images of it on the web? Better still, are there gifs or videos that show it rotating in a way that brings its three-dimensionality to the fore? I ask because this seems like a nice way of looking at a hypercube (leaving aside the defect that two of the vertices of the hypercube coincide). Jim Propp

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[math-fun] (no subject)
by Bob Mayans 14 May '18

14 May '18

http://general.myglenwoodhomes.com Bob Mayans

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[math-fun] What is this function? puzzle
by Bill Gosper 12 May '18

12 May '18

Wow. Experimentally, it's also x+1 for -1≤x≤0, -x-1 for -2≤x≤-1, and √(1-2x-x²) for -3≤x≤-2, wherein it goes imaginary. gosper.org/puzfn.png It can probably be guessed anywhere. Where has it been proven? Note the tiny flat spot in the imaginary part near x = -3.5. --rwg On 2018-05-12 03:54, James Propp wrote: > Could f be a polynomial? Assuming deg f is at least 1, Joerg’s equation > implies 2 deg f = 1 + def f, so we’ll need def f = 1. Putting f(x) = ax+b > in Joerg’s equation, we get (ax+b)^2 - 1 = x (ax+a+b), or > > (a^2) x^2 + (2ab) x + (b^2 - 1) = (a) x^2 + (a+b) x, > > with unique solution a=b=1. > > So I’m guessing f(x) = x+1. > > Jim Propp > > On Saturday, May 12, 2018, Joerg Arndt <arndt(a)jjj.de> wrote: > >> f(x)^2 - 1 = x * f(x+1) >> No idea how to proceed from there, though. >> >> Best regards, jj >> >> >> * Dan Asimov <dasimov(a)earthlink.net> [May 05. 2018 08:20]: >> > Define a function f : [0,oo) —> R via >> > >> > f(x) = sqrt(1 + x*sqrt(1 + (x+1)*sqrt(1 + (x+2)*sqrt(1+... >> > >> > Evaluate f(x) in closed form. >> > >> > —Dan

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[math-fun] What is this function? puzzle
by Dan Asimov 12 May '18

12 May '18

Define a function f : [0,oo) —> R via f(x) = sqrt(1 + x*sqrt(1 + (x+1)*sqrt(1 + (x+2)*sqrt(1+... Evaluate f(x) in closed form. —Dan

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[math-fun] "The Busy Bee"
by James Propp 11 May '18

11 May '18

This may be a folie-a-deux, but both Serge Troubetzkoy and I have recollections of my having written a preprint that neither of us can find any trace of in the on-line or off-line universe. It was called "The Busy Bee", and it was a follow-up to my articles in the Mathematical Intelligencer (cowritten with David Gale, Scott Sutherland, and Serge Troubetzkoy) on the Langton Ant and variations thereon. The article was about what happens when you replace the square grid of the Langton Ant by an hexagonal grid. As in the square grid case, you can set up the rules and the initial conditions so that the bee builds ever-larger symmetrical structures in its universe. Well, sort of. I was able to prove that bilateral symmetry reasserts itself infinitely often, but I was never able to show that the structures grow without bound. That is: I wasn't able to rule out the possibility that at some point the structures start to shrink and the universe returns to its initial configuration. Does anyone have a copy of this article? (I'm guessing that I wrote it as a preprint, then discovered that my results were already in work of E.G.D. Cohen, and then let it languish.) Jim Propp

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[math-fun] Fwd: Fill in the blank.
by rwg 11 May '18

11 May '18

gosper.org/√blank.png --rwg

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[math-fun] Spam subject line typo implies disturbing alternative
by Marc LeBrun 10 May '18

10 May '18

Spam subject line typo implies disturbing alternative: "Discrete, Beautiful, Women Waiting For You"

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[math-fun] Musical parallelotopes, climbable tesseracts, etc.
by James Propp 09 May '18

09 May '18

Do any of you know of passages of music that represent 2-dimensional projections of 3- or higher-dimensional parallelotopes if one plots time against the log of frequency? A simple way to generate such a passage is to start with a two-note figure. Create a four-note figure consisting of the original two-note figure followed by a transposed version of same. Now create an eight-note figure consisting of that four-note figure followed by a transposed version of same. The eight notes can be conceived of as the vertices of a musical parallelohedron (projected into a 2D space). Apply the construction again and you’ve got a sixteen-note projection of the vertices of a 4D parallelotope. (More interesting variants exist, but that’s the basic idea.) Has this sort of geometrically-inspired scheme for organizing pitches in time been exploited by any composers to create music worth listening to? I ask because I’m working on an essay about the hypercube, so musical embodiments would fit in nicely. For that matter, has anyone built a 3D jungle gym based on 4D structures? (As I’ll mention in the article, jungle gyms were invented by the same guy who coined the term “tesseract”, and the idea of making higher dimensions more kinesthetically accessible was a goal of his.) Thanks, Jim Propp

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[math-fun] A review of using cell phone email in Albuqerque
by Hilarie Orman 09 May '18

09 May '18

The app, Is crap. The service, Worse. Hilarie --- "Nevertheless, she persisted."

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Re: [math-fun] math-fun Digest, Vol 183, Issue 17
by Hilarie Orman 08 May '18

08 May '18

----- Original Message ----- From: math-fun-request(a)mailman.xmission.com To: math-fun(a)mailman.xmission.com Sent: Mon, 07 May 2018 12:00:02 -0600 (MDT) Subject: math-fun Digest, Vol 183, Issue 17 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..."

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