[math-fun] Re Iterated averaging of triples
This reminds me of a paper Elwyn Berlekamp wrote in (I think) the American Mathematical Monthly a long time ago.
Neil, Is this the paper you're thinking of? Berlekamp, E. R., E. N. Gilbert, and F. W. Sinden. "A polygon problem." The American Mathematical Monthly 72.3 (1965): 233-241. On Fri, Sep 18, 2020 at 3:30 PM Neil Sloane <njasloane@gmail.com> wrote:
This reminds me of a paper Elwyn Berlekamp wrote in (I think) the American Mathematical Monthly a long time ago. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Victor, I'm not certain that is the paper. The drawings don't match what I remember. On Fri, Sep 18, 2020 at 3:41 PM Victor Miller <victorsmiller@gmail.com> wrote:
Neil, Is this the paper you're thinking of?
Berlekamp, E. R., E. N. Gilbert, and F. W. Sinden. "A polygon problem." The American Mathematical Monthly 72.3 (1965): 233-241.
On Fri, Sep 18, 2020 at 3:30 PM Neil Sloane <njasloane@gmail.com> wrote:
This reminds me of a paper Elwyn Berlekamp wrote in (I think) the
American
Mathematical Monthly a long time ago. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
That paper has good examples, but I didn’t see an answer about conditions for a circular limit. Conditions would probably have to take into account link topology (my previous attempt to score distributions did not), but is it possible that no simple condition exists? Another idea is to look at projections of the state vector onto eigenvectors of the smoothing matrix, but I haven’t yet. This problem “given a large number of random points and a link topology, predict the outcome without iterating” is interesting to me. Any thoughts? —Brad
On Sep 18, 2020, at 3:36 PM, Neil Sloane <njasloane@gmail.com> wrote:
Victor, I'm not certain that is the paper. The drawings don't match what I remember.
On Fri, Sep 18, 2020 at 3:41 PM Victor Miller <victorsmiller@gmail.com> wrote:
Neil, Is this the paper you're thinking of?
Berlekamp, E. R., E. N. Gilbert, and F. W. Sinden. "A polygon problem." The American Mathematical Monthly 72.3 (1965): 233-241.
On Fri, Sep 18, 2020 at 3:30 PM Neil Sloane <njasloane@gmail.com> wrote:
This reminds me of a paper Elwyn Berlekamp wrote in (I think) the American Mathematical Monthly a long time ago. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
participants (3)
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Brad Klee -
Neil Sloane -
Victor Miller