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Pi Approximation Day
07-25-2019, 01:26 PM (This post was last modified: 07-26-2019 01:34 PM by Albert Chan.)
Post: #21
RE: Pi Approximation Day
Best Pi approximation using decimal digits permutations:

85910 / 27346 = 355 / 113 ≈ 3.141592920, abs error ≈ 2.67e-7

Proof:

Since 355/113 is one of Pi's convergents, and the next convergent is 103993/33102
A better ratio, if exist, must be a semi-convergent: (52163+355k)/(16604+113k), k>=0

(52163+355k) + (16604+113k) (mod 9) ≡ 7 ≠ 0

Thus, better ratio does not exist.

Update: With hex digits permutations, this produce best pi approximation

0xFE86C29B / 0x5104AD73 = 4270244507 / 1359261043 ≈ 3.141592653590, abs error ≈ 2.94e-13
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Messages In This Thread
Pi Approximation Day - Gerson W. Barbosa - 07-22-2019, 03:41 AM
RE: Pi Approximation Day - ggauny@live.fr - 07-22-2019, 10:01 AM
RE: Pi Approximation Day - burkhard - 07-22-2019, 01:02 PM
RE: Pi Approximation Day - rprosperi - 07-22-2019, 01:05 PM
RE: Pi Approximation Day - Albert Chan - 08-14-2019, 10:46 PM
RE: Pi Approximation Day - Albert Chan - 08-15-2019, 03:38 AM
RE: Pi Approximation Day - Claudio L. - 07-22-2019, 07:48 PM
RE: Pi Approximation Day - Dave Shaffer - 07-23-2019, 05:07 PM
RE: Pi Approximation Day - ijabbott - 07-23-2019, 05:18 PM
RE: Pi Approximation Day - jebem - 07-24-2019, 06:03 AM
RE: Pi Approximation Day - bshoring - 07-22-2019, 09:40 PM
RE: Pi Approximation Day - BartDB - 07-23-2019, 05:31 PM
RE: Pi Approximation Day - BartDB - 07-24-2019, 10:30 AM
RE: Pi Approximation Day - ijabbott - 07-23-2019, 05:09 PM
RE: Pi Approximation Day - Erwin - 07-23-2019, 08:26 PM
RE: Pi Approximation Day - Albert Chan - 07-25-2019 01:26 PM
RE: Pi Approximation Day - Bill Duncan - 07-26-2019, 11:02 PM
RE: Pi Approximation Day - Leviset - 08-14-2019, 09:36 PM



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