[math-fun] CF inconsequentia
(Very good news, if no news is good news.) I once had a jugendtraum of showing the continued fraction of π to be aperiodic mod 2 by analyzing the process of converting one of its non-regular continued fractions to its regular one. I just looked at the simpler problem of converting 1+1/(2+2/(3+3/... to 1/(e-1). It appears that its rate of convergence is incommensurable with 2,6,10,14,. . . = coth(1/2). This should enable me to prove the geezertraum that e and e are algebraically independent. Furtherless, if x has CF = 0,1,4,9,16, ..., then (1+x)/(1-x) has quasiperiod 8, with 4 constant terms and 4 quadratics. (No linears.) —rwg
Yup, that's what he meant! WFL On 1/24/19, James Propp <jamespropp@gmail.com> wrote:
On Thursday, January 24, 2019, Bill Gosper <billgosper@gmail.com> wrote:
This should enable me to prove the
geezertraum that e and e are algebraically independent.
What did you mean to write here?
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
geezer + traum (german for dream) = geezertraum seems to be the construct On Thu, Jan 24, 2019 at 8:47 AM Fred Lunnon <fred.lunnon@gmail.com> wrote:
Yup, that's what he meant! WFL
On 1/24/19, James Propp <jamespropp@gmail.com> wrote:
On Thursday, January 24, 2019, Bill Gosper <billgosper@gmail.com> wrote:
This should enable me to prove the
geezertraum that e and e are algebraically independent.
What did you mean to write here?
Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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-- Thane Plambeck tplambeck@gmail.com http://counterwave.com/
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