Re: 2.058833711777943011170351... = ? continued fraction convergents//


Proginoskes wrote:
don.lotto@xxxxxxxxxxxxxxx wrote:
don.lotto@xxxxxxxxxxxxxxx wrote:
N. Silver wrote:
Proginoskes wrote:

2 + (1 / (17 - (1 / (340 - (1 / (8.5 + (1 / 51))))))) = 2.05883371

fermat gauss numbers on casio fx 82 schools calc.
from memory. signs may be wrong.

Exact value: 2.058833712. No good.

regular n-gon.
multiples 2 3 5 17
= 2^(2^n) +1.

Re: 2.058833711777943011170351... = ? continued fraction convergents//

I tried that, but I guess I didn't mention it. The continued fraction
starts out as
[2, 16, 1, 338, 1, 7, 2, 1964179, 1, 1, 8, 169, 1, 3, 1, 6,
22000684073033, ...]

That's a humungous element for your continued fraction. The part you
quoted only
gave [2, 16, 1, 338, 1, 7, 2, 1964179, 1, 1, 4]. Is the number defined
in terms of
its continued fraction? Or did you really do your calculations to 60
digits or so?
The difference between [2, 16, 1, 338, 1, 7, 2, 1964179, 1, 1, 8, 169,
1, 3, 1, 6,
22000684073033] and [[2, 16, 1, 338, 1, 7, 2, 1964179, 1, 1, 8, 169, 1,
3, 1, 6,
22000684073032] is less than 5.8 * 10^(-60).

Robert Israel israel@xxxxxxxxxxx
Department of Mathematics http://www.math.ubc.ca/~israel
University of British Columbia Vancouver, BC, Canada

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