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Happy Pi Day!
03-15-2017, 03:57 PM (This post was last modified: 03-15-2017 10:42 PM by Gerson W. Barbosa.)
Post: #12
RE: Happy Pi Day!
(03-15-2017 11:04 AM)franz.b Wrote:  355/113 is enough for me B-)

That's perhaps the most efficient rational approximation for \(\pi\): six digits in a mnemonic sequence giving seven correct digits.

The 1762-digit fraction below gives only 707 digits (perhaps a few more) and is somewhat hard to memorize.

------------------------------

707

« PUSH RAD -105 CF -3 CF DUP .653 * 1.74 + IP R→I DUP 2 MOD + DUP 4 * OVER DUPDUP 1 - 1
FOR i i SQ SWAP / PICK3 + ROT SWAP -1
STEP INV NIP UNROT + 1 - 3 0 UNROT
FOR i i INV i 2 - INV - + -4
STEP - 4 * EXPAND →STR "'" "" SREPL ROT DROP2 POP
»

:s: 1274.5305 (time on my iPhone)

35471270118869764571868355345605539644932682747073948595148728173396218838668496​80716426124902558473273344718040678263223310007300548098446944940735563175195185​79323304238108709671904418651693017693336383731106603027004914829454445857328201​05924605428311002761716473437615659392155761487611060526868601273453231898921986​03346750895370582643794723222113030733123697513779494958569010520916965922261361​50912781934736718101804617138969374612667021145232878466424131101366141969361769​76029123163627319062908158192243507523352526680253139185385238035253759673955361​64753305772996193396743873266368301326861081810651321062825642235467130083886694​29978624344603656750671217335693097846544875989492305955191455496667840796358958​54318597270213456322812296404622832012961138994524991861828477269161456938399075​36641613518969979837287818614714737709619011495381477179300261556327556859088076​8
/
11290855954331929765162875991672337005763900233129789215007366526465816927928074​99910519051390719630100518054981495532402000479709747220290019459549698290971530​80519808598234473145589659408612308338495967787945281300419514221238758104012207​91617778874064429696755480283483475358841356899944430809069589392140510992481520​00826115469277539329220641057707652808895534744233006721848321578069349072611507​65976928124031425881129023075006910569280746723187915395363232463456021210395860​67513765201530999299014996124193701700437357615236050277051928851200804664427103​09230073374186050477298794155770558099350191823502206767887178212506347749784516​42170205919755951022290456573354203993293526964682167478504255902556770952397557​10260367678979941803636081060659736127271086039016609855284050676165107007788796​80847217941144275687554984641214388815408615188638900225501578409931091369249187​5

------------------------------

Edited to add a missing 's'.
Edited again per Valentin's observation below.
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Messages In This Thread
Happy Pi Day! - Gerson W. Barbosa - 03-14-2017, 01:14 AM
RE: Happy Pi Day! - Ángel Martin - 03-14-2017, 06:17 AM
RE: Happy Pi Day! - Csaba Tizedes - 03-14-2017, 08:22 AM
RE: Happy Pi Day! - Dave Britten - 03-14-2017, 12:47 PM
RE: Happy Pi Day! - Eddie W. Shore - 03-14-2017, 01:06 PM
RE: Happy Pi Day! - jebem - 03-14-2017, 01:22 PM
RE: Happy Pi Day! - Eddie W. Shore - 03-14-2017, 01:24 PM
RE: Happy Pi Day! - Gerson W. Barbosa - 03-14-2017, 03:50 PM
RE: Happy Pi Day! - Gerson W. Barbosa - 03-14-2017, 05:07 PM
RE: Happy Pi Day! - Joe Horn - 03-15-2017, 11:33 PM
RE: Happy Pi Day! - Gerson W. Barbosa - 03-16-2017, 12:06 AM
RE: Happy Pi Day! - d b - 03-15-2017, 02:53 AM
RE: Happy Pi Day! - franz.b - 03-15-2017, 11:04 AM
RE: Happy Pi Day! - Gerson W. Barbosa - 03-15-2017 03:57 PM
RE: Happy Pi Day! - Valentin Albillo - 03-15-2017, 08:56 PM
RE: Happy Pi Day! - Gerson W. Barbosa - 03-15-2017, 10:50 PM
RE: Happy Pi Day! - EdS2 - 03-17-2017, 10:00 PM
RE: Happy Pi Day! - Gerson W. Barbosa - 03-18-2017, 02:17 AM
RE: Happy Pi Day! - Joe Horn - 03-18-2017, 03:43 AM
RE: Happy Pi Day! - Gerson W. Barbosa - 03-18-2017, 09:17 PM
RE: Happy Pi Day! - ttw - 03-16-2017, 01:22 AM
RE: Happy Pi Day! - pier4r - 03-28-2017, 10:30 AM
RE: Happy Pi Day! - Joe Horn - 03-28-2017, 11:59 AM
RE: Happy Pi Day! - pier4r - 03-28-2017, 09:23 PM



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