May 2007 - mathfun@mailman.xmission.com

[math-fun] Reverse date factors
by Eric Angelini 02 May '07

02 May '07

Hello Math-Fun, One can produce an integer by concatenating the digits spelling a full date -- example for today, May 2nd, 2007: --> 20070502 This 8-digit integer can be represented like this: abcdefgh. I was wondering if there exist a (close) date fulfilling this: abcdefgh = h*g*f*e*d*c*b*a where as many * as one wishes can be deleted. (but not all of them! -- concatenate accordingly to produce a sound set of factors. For instance: abcdefgh = hgfe*d*c*b*a or abcdefgh = h*g*f*edcba or abcdefgh = hg*f*e*d*c*b*a ... Best, É. (I think the "direct" equality is impossible: abcdefgh = a*b*c*d*e*f*g*h)

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[math-fun] two letters by george mackey sent to then college sophomore stephanie frank singer, ca 1982
by Thane Plambeck 02 May '07

02 May '07

I thought these were interesting http://www.symmetrysinger.com/Mackey/letter1.pdf http://www.symmetrysinger.com/Mackey/letter2.pdf -- Thane Plambeck tplambeck(a)gmail.com http://www.plambeck.org/ehome.htm

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Re: [math-fun] Mathematica 6 launched
by Richard Schroeppel 02 May '07

02 May '07

(This is from wouter.meeussen(a)pandora.be; for some reason the mailing list filter didn't like it. --Rich) ------------------------------ just screened the website, still no ConvexHull3D ? was promissed in Weinstein's ecyclopedia! "... Future versions of Mathematica will support -dimensional convex hulls." hmmm. Wouter. ----- Original Message ----- From: "Ed Pegg Jr" <ed(a)mathpuzzle.com> To: "math-fun" <math-fun(a)mailman.xmission.com> Sent: Tuesday, May 01, 2007 9:01 PM Subject: [math-fun] Mathematica 6 launched > I wrote a column about the just-launched Wolfram Demonstrations Project. It has over 1200 interactive mathematical demonstrations. > > http://www.maa.org/editorial/mathgames/mathgames_05_02_07.html > > And... Mathematica 6 has launched. Lots of new capabilities. > > http://www.wolfram.com/products/mathematica/index.html > > Ed Pegg Jr >

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Re: [math-fun] Topology puzzle
by Michael Reid 01 May '07

01 May '07

oops! yes, that should be the complete bipartite graph K_3,3 , as dan notes. mike > > Determine whether or not the topological space Y x Y > > (the cartesian product of two Y-shaped spaces, each > > the union of 3 closed intervals) can be embedded as > > a subset of 3-space. > > it cannot be embedded. Y x Y is homeomorphic to the cone over > the graph C_3 x C_3 . if there were such an embedding, intersecting > with a small sphere centered at the vertex (the point (y_0, y_0) > in Y x Y , where y_0 is the branch point of Y ) would give an > embedding of C_3 x C_3 in the sphere. this is impossible, because > this graph is non-planar. > >> > > Except for the fact that I would say the graph that Y x Y is a > cone over is K(3,3), that is exactly my conclusion, and my reasoning. > (By the Leibniz rule, > > bd(Y x Y) = bd(Y) x Y u Y x bd(Y), > > (with agreement on bd(Y) x bd(Y)) -- which is homeomorphic to K(3,3).) > > (This is quite clearly valid for Y x Y embedded either smoothly > or as a simplicial complex. There may be some bothersome > technical details to check, however, if the embedding is only > known to be continuous.) > > --Dan

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[math-fun] pi to 500 digits on piano
by Thane Plambeck 01 May '07

01 May '07

I can't decide if it's the F major drone in the accompaniment or the (human determined?) rests that makes this so musical: http://www.tomdukich.com/math%20pi%20piano%20keyboard.html -- Thane Plambeck tplambeck(a)gmail.com http://www.plambeck.org/ehome.htm

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Re: [math-fun] Topology puzzle
by Daniel Asimov 01 May '07

01 May '07

Mike Reid writes: << [I asked]: > Determine whether or not the topological space Y x Y > (the cartesian product of two Y-shaped spaces, each > the union of 3 closed intervals) can be embedded as > a subset of 3-space. it cannot be embedded. Y x Y is homeomorphic to the cone over the graph C_3 x C_3 . if there were such an embedding, intersecting with a small sphere centered at the vertex (the point (y_0, y_0) in Y x Y , where y_0 is the branch point of Y ) would give an embedding of C_3 x C_3 in the sphere. this is impossible, because this graph is non-planar. >> Except for the fact that I would say the graph that Y x Y is a cone over is K(3,3), that is exactly my conclusion, and my reasoning. (By the Leibniz rule, bd(Y x Y) = bd(Y) x Y u Y x bd(Y), (with agreement on bd(Y) x bd(Y)) -- which is homeomorphic to K(3,3).) (This is quite clearly valid for Y x Y embedded either smoothly or as a simplicial complex. There may be some bothersome technical details to check, however, if the embedding is only known to be continuous.) --Dan

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Re: [math-fun] Topology puzzle
by Michael Reid 01 May '07

01 May '07

> Determine whether or not the topological space Y x Y > (the cartesian product of two Y-shaped spaces, each > the union of 3 closed intervals) can be embedded as > a subset of 3-space. it cannot be embedded. Y x Y is homeomorphic to the cone over the graph C_3 x C_3 . if there were such an embedding, intersecting with a small sphere centered at the vertex (the point (y_0, y_0) in Y x Y , where y_0 is the branch point of Y ) would give an embedding of C_3 x C_3 in the sphere. this is impossible, because this graph is non-planar. mike

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[math-fun] math and memory
by James Propp 01 May '07

01 May '07

Steve Rowley writes: >Strangely, and somewhat embarassingly, there's an appendix in my old >thesis on approximately this problem. There are lots of anecdotes in mathematics about mathematicians in later life who've forgotten about work they did earlier. (I think the archetype involves Hilbert hassling a seminar-speaker about some result he used that Hilbert thought wasn't believable, and the speaker responding "Not only is it true, but you're the one who proved it!") And I'm now old enough (47) to have begun to experience this phenomenon first-hand in myself. Question: Is this phenomenon unique (or at least strongest) in math, as opposed to other scientific and/or creative disciplines? I think research in math is about building up intuitions in some mathematical domain and combining those intuitions with the tools in one's technical toolkit to solve some problems in that domain. The trouble is that intuitions have a short half-life, so even if you keep your mental tools from rusting, work you did a decade or two ago is going to seem unfamiliar, and work you did three or four decades ago might seem like the work of another person. I suspect that other fields are more intuitive, and that the projects one completes there sink deeper hooks into memory, because they are more rooted in physical reality, personal history, etc. What do you all think? (And has anyone studied the phenomonon across disciplines?) Jim Propp

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[math-fun] sunday funnies
by Schroeppel, Richard 01 May '07

01 May '07

A factoring cartoon. --Rich http://xkcd.com/c247.html

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[math-fun] Topology puzzle
by Daniel Asimov 01 May '07

01 May '07

Topology puzzle: Determine whether or not the topological space Y x Y (the cartesian product of two Y-shaped spaces, each the union of 3 closed intervals) can be embedded as a subset of 3-space. --Dan

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