May 2011 - mathfun@mailman.xmission.com

[math-fun] Dan asks: MathCad -- do you like it?
by rcs＠xmission.com 24 May '11

24 May '11

This is from Dan Asimov. --Rich ------------- Date: Mon, 16 May 2011 17:10:16 -0700 (GMT-07:00) Subject: MathCad -- do you like it? From: Dan Asimov <dasimov(a)earthlink.net> To: math-fun <math-fun(a)mailman.xmission.com> I've been asked my opinion of MathCad as a tool, but as I had to say, I have no experience with it. But among those of you who do, anything you can say on these points will be much appreciated: * What is your overall opinion of it and why? * In particular, to what extent does it have a wide range of mathematical applications? * What kinds of math graphics might you have noticed to be beyond its capabilities? Please note: @ Anything you write will not be attributed to you (or even to math-fun), but rather described as what "members of a group of my smart friends" said. @ If you respond, please let me know if you prefer *not* to be quoted directly. Otherwise I may be lazy and just copy some or all of what you wrote into my summary. Thanks, Dan

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Re: [math-fun] spinorial egg
by Dan Asimov 24 May '11

24 May '11

The coolest example of this imo would be a purely mechanical sphere -- lets say opaque -- that displayed spinorial behavior because of some clever arrangement of its insides. A start might be a sphere with several smaller spheres inside it. Its state, as measured by the motion of the spheres inside, depends not only on the rotational position of the outer sphere, but on its path of rotations. Dan -------------- Bill T. wrote: << Obviously it *could* be done. I imagine that it wouldn't be hard for an iphone developer to write an iphone app that would do this . . . >> On May 22, 2011, at 9:57 AM, James Propp wrote: >> Has anyone built a macroscopic object that has spinorial behavior[?] [as has been noted: I.e., its state (like color and/or sound) -- after it goes through a continuous path P of rotations, starting from the identity -- is not determined by rotational position alone. Instead it's determined by the lift of P from SO(3) to its Lie-group double cover: Spin(3) ~~ SU(2) == S^3 --d.a.] I envision an egg that emits a hum when it's resting on its base and is in the correct spinorientation. Rotate it 360 degree about any axis: no hum. Rotate it again about any axis: it hums. >> Sometimes the brain has a mind of its own.

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[math-fun] spinorial egg
by James Propp 23 May '11

23 May '11

Has anyone built a macroscopic object that has spinorial behavior but is not tethered to a frame by strings or ropes? (For an example of what I don't mean, see Ethan Bolker's article "The Spinor Spanner".) I envision an egg that emits a hum when it's resting on its base and is in the correct spinorientation. Rotate it 360 degree about any axis: no hum. Rotate it again about any axis: it hums. It's okay with me if the egg's mechanism "tethers" it via electromagnetic waves to an external device that tracks it in 3D and tells it when to hum. It's also okay with me if the egg isn't an egg but a sphere or cube (or a doll resembling P. A. M. Dirac). Jim Propp

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Re: [math-fun] An Abelian grape
by Michael Kleber 21 May '11

21 May '11

On May 21, 2011 11:08 AM, "Adam P. Goucher" <apgoucher(a)gmx.com> wrote: > > After reading about the Abelian grape, I decided to make a few myself: > > > Q: What's yellow and equivalent to the Axiom of Choice? > A: Zorn's Lemon > > (Unfortunately, I have been beaten to this one, according to MathWorld!) By decades, yes. > > Q: What's green and has a real product? > A: Conjugate pear Nice! It is flawed when delivered aloud, though, because it tales work, even in context, to decode the homophone. > > Q: What's yellow and can be rearranged into two copies of itself? > A: Banana-Tarski Paradox I think this is dominated by the "great new anagram" B-T P joke. Also, the paradox itself isn't what can be so rearranged, though your joke could be adjusted to compensate. > > Q: What's light green and a subspace of the complex plane? > A: Real lime The canonical variant here is "What is green, far away, and compactifies the real plane? A: The lime at infinity." --Michael _______________________________________________ > math-fun mailing list > math-fun(a)mailman.xmission.com > http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun

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[math-fun] An Abelian grape
by Adam P. Goucher 21 May '11

21 May '11

After reading about the Abelian grape, I decided to make a few myself: Q: What's yellow and equivalent to the Axiom of Choice? A: Zorn's Lemon (Unfortunately, I have been beaten to this one, according to MathWorld!) Q: What's green and has a real product? A: Conjugate pear Q: What's yellow and can be rearranged into two copies of itself? A: Banana-Tarski Paradox Q: What's light green and a subspace of the complex plane? A: Real lime Sincerely, Adam P. Goucher

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[math-fun] Josh Jordan + AuntBeast defeat Roman Khorkov in Sprouts world championship
by Thane Plambeck 16 May '11

16 May '11

Here's a brief writeup http://www.wgosa.org/clash2011c.htm Here's analysis of one game by Josh http://www.files.takingthefun.com/sprouts/2011clashgame1/ -- Thane Plambeck tplambeck(a)gmail.com http://counterwave.com/

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[math-fun] Josh Jordan + AuntBeast defeat Roman Khorkov in Sprouts world championship
by Thane Plambeck 16 May '11

16 May '11

Here's a brief writeup http://www.wgosa.org/clash2011c Here's analysis of one game by Josh http://www.files.takingthefun.com/sprouts/2011clashgame1/ -- Thane Plambeck tplambeck(a)gmail.com http://counterwave.com/

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Re: [math-fun] the $24 million dollar book on Amazon
by bobmayans＠aol.com 16 May '11

16 May '11

This is not as spectacular, but I found on a bookseller website a copy of Andre Cheron's volumes on chess endgames, at a very reasonable price of 12.50 -- but when I started to purchase it, they meant $12,500. It turns out that it was Bobby Fischer's copy and had lots of annotations, and is no doubt very valuable to someone else. Bob Mayans

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Re: [math-fun] Atomtrap
by Dan Asimov 16 May '11

16 May '11

now that I've downloaded the link, it appears to be designed to work on PC's but not Macs -- is that right? Too bad, because I have only Macs (and no PC emulator). --Dan Adam wrote: << Here's a PSPACE-complete puzzle game I created, if anyone is interested: . . . You can design your own levels (and upload!), which can be as complex as any linear-bounded automaton (Turing machine with bounded memory). One of my default levels contains a 15-puzzle built into it. >> Sometimes the brain has a mind of its own.

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[math-fun] A gasket "application"
by Bill Gosper 16 May '11

16 May '11

http://gosper.org/fst.pdf (pp130-131, 137) shows how to construct the Fourier series for m copies of an arc z(t), -1<=t<=1, arranged around a regular m-gon. Replacing m by -m flips the arcs across the corresponding sides of the m-gon. Or more likely, rotates the arcs by pi about the centers of the sides of the m-gon, and then sweeps them in the opposite order. Using my peculiar 2x2 matrix product for the Sierpinski gasket Fourier series, m=6 makes a spongy star of David, and -6 makes a lace doily. But what I really wanted was six gaskets pointing alternately in and out, which makes the boundary of the region of the complex plane represented by the base 2 pure fractions, using the digits 0, 1, (-1)^(2/3), and (-1)^(4/3) ! (http://www.tweedledum.com/rwg/rad2.htm, Mandelbrot calls (part of) this the Arrowhead Fractal.) Unable to salvage my spastic attempts, Julian finally found the general "inny-outy" transformation, after a 12 hr struggle. ( http://gosper.org/sierpclock.png http://gosper.org/base2sierp.png) Since we were unable to rederive my 2x2 product, Julian also derived for good measure a 3x3 (with 9^-n convergence vs my 3^-n). We have yet to demonstrate their equivalence. Presumably, these (infinite) series (exactly) represent a "space"fill of the closed version of the D=lg 3 gasket fractal. (Which, if accurately drawn, is completely invisible, since it has zero area. Unless it is implicit as the boundary of a 2D region.) The six-gasket boundary arc appears to have uncountably many double points, and one triple point. Spacefilling any set makes it an arc. Unlike the gasket, many such sets, with 1<=dimension<2, can be spacefilled 1-1. The "open" gasket, constructed by deleting closed triangles from a open one, is a countable intersection of open sets. Is it actually open? --rwg

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