October 2010 - mathfun@mailman.xmission.com

[math-fun] breakthrough in linear algebra
by Simon Plouffe 22 Oct '10

22 Oct '10

Hello, some people at Carnegie Mellon found a way to speed up a lot linear equations : http://www.cmu.edu/news/archive/2010/October/oct21_speedyalgorithm.shtml if true, this is going to be interesting for many algorithms. I did not verified, it is certainly worth a lookup, have a nice day, best regards, simon plouffe

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Re: [math-fun] breakthrough in linear algebra
by Daniel Asimov 22 Oct '10

22 Oct '10

P.S. Let's see: the planarity criterion is that the graph must not contain a subset that is topologically either the water-gas-electricity graph K(3,3) or the complete graph K(5) on 5 nodes. Hmm, so I wonder how this criterion may be reflected in the invariants of the graph's connectivity matrix. These graphs K(3,3) and K(5) have connectivity matrices: 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 1 1 1 0 0 0 1 1 1 0 0 0 1 1 1 0 0 0 and 0 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 0 1 1 1 1 1 0 and one or the other of these would have to be -- roughly speaking -- a submatrix of any non-planar graph. But I'm too rushed to figure out their eigenvalues right now. --Dan Henry wrote: << . . . Interestingly, _planar graphs_ play a part in this paper! Who knew that linear algebra & planar graphs were connected ? . . . >> _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele

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Re: [math-fun] breakthrough in linear algebra
by Daniel Asimov 22 Oct '10

22 Oct '10

Henry wrote: << . . . Interestingly, _planar graphs_ play a part in this paper! Who knew that linear algebra & planar graphs were connected ? . . . >> Actually, any graph G can be defined by its connectivity matrix M = (m_ij), with m_ij = 1 if an edge connects nodes i and j, and 0 if not. Then there is the question of how the invariants of M, like its eigenvalues, are related to topological properties of G. This may not seem very closely fetched, but evidently people have got a lot of mileage out of it. --Dan _____________________________________________________________________ "It don't mean a thing if it ain't got that certain je ne sais quoi." --Peter Schickele

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Re: [math-fun] breakthrough in linear algebra
by Henry Baker 22 Oct '10

22 Oct '10

I have every confidence in Gary Miller. The actual paper is available from the link below, or directly from: http://www.cs.cmu.edu/~glmiller/Publications/Papers/KoutisApproaching-2010.… Interestingly, _planar graphs_ play a part in this paper! Who knew that linear algebra & planar graphs were connected ? I guess the next practical question is whether this algorithm can be parallelized to any significant degree. At 07:28 AM 10/22/2010, Simon Plouffe wrote: >Hello, > > some people at Carnegie Mellon found a way to speed up >a lot linear equations : > >http://www.cmu.edu/news/archive/2010/October/oct21_speedyalgorithm.shtml > >if true, this is going to be interesting for many algorithms. > >I did not verified, it is certainly worth a lookup, > > have a nice day, > best regards, > > simon plouffe

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Re: [math-fun] Martin Gardner archive
by James Propp 21 Oct '10

21 Oct '10

Since Gardner, in his letter to Klarner dated April 16, 1990, says that a friend wrote to him about the two tilings problems a month or two earlier, and since Conway and Lagarias' article on the same subject came out that same year, I think we can safely rule out the possibility that Conway and/or Thurston learned about the problem from Gardner. (Alas; it would've made a nice story about Gardner's impact on mathematics.) Jim Propp

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Re: [math-fun] Museum of Mathematics
by James Propp 19 Oct '10

19 Oct '10

Robert Munafo (mrob27(a)gmail.com) writes: >Here are two things I have been working on. Both sound great! Here's something that I fantasize about in a similar vein: I picture a big touch-sensitive panel, five feet wide and stretching up to the ceiling. In one mode, it runs a big simulation of Life, and you can pause the action, toggle the states of specific bits with your fingers (perhaps referring to a nearby card that lists common fun configurations to insert into the Life universe), and then re-start the simulation to see what happens. In another mode, the panel runs a 1-D cellular automaton, drifting up the screen as it evolves. The way the panel disappears into the ceiling is integral to the "wow" effect I'd want to achieve. A big touch-sensitive wall might have other cool uses. For instance, I have a great app on my iPhone that lets me zoom in on the Mandelbrot set and various associated Julia sets, using the wonderful two-finger expand/contract gesture. (It almost makes me fancy that the iPhone was invented by someone who wanted to explore the Mandelbrot set in this very tactile way, and decided to invent a PDA that would let him do it!) It'd be good to have a user-controlled way to zoom in the Koch snowflake curve and the Weierstrass function and Bolzano's function (the first example of an everywhere-continuous, nowhere-differentiable function). Jim Propp

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[math-fun] continuous Galton board
by James Propp 19 Oct '10

19 Oct '10

Bob Baillie (rjbaillie(a)frii.com) writes: >one had ping pong balls (or marbles?) falling down through a grid of pegs >that caused the paths to become random. at the bottom, a bell-shaped curve >gradually formed as more and more balls collected there. Could one make a Galton board modeling continuous deterministic flow (as opposed to discrete random flow), using a liquid? And has anyone done this? I picture a triangular array of buckets, with water being pumped into the the top pocket, from which water overflows into the two buckets beneath it on either side, from which water overflows, etc. Jim Propp

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[math-fun] Magic by Numbers
by Marc LeBrun 19 Oct '10

19 Oct '10

Amusing observations; from the NYT no less: http://www.nytimes.com/2010/10/17/opinion/17gilbert.html ³Well, on the one hand, most people have five fingers, and on the other hand, most people have five more.²

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[math-fun] PPS Re: Museum of Mathematics
by Dan Asimov 18 Oct '10

18 Oct '10

P.P.S. I neglected to make clear that the reason I mentioned David Gale's and Richard Palais's projects is that least some of their exhibits may be amenable to being adapted for the Museum of Mathematics. --Dan Daniel Asimov Visiting Scholar Department of Mathematics University of California Berkeley, California

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Re: [math-fun] Re : 312 = Black Hole
by Eric Angelini 18 Oct '10

18 Oct '10

Gareth: > *Two* things are special in the 10/even/odd case: we always reach the same cycle, and that cycle has length 1. I think the best generalization is "describe other situations where there is a unique such cycle and it has length 1". --------------------------------------------------------------- Hello, I think I have one: "Sixteen, seven, nine" There are indeed 16 letters all together in the above line with 7 even-rank-in-the-alphabet letters (..xt..n, ..v.n, n.n.) 9 odd-rank-in-the-alphabet letters (si..ee., se.e., .i.e) Don't know if this is the unique such fixed point... Best, É.

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