Timeline for Integral representation of $\frac{355}{113}-\pi$? [duplicate]
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jun 26, 2022 at 17:01 | history | closed |
Francois Ziegler Gerald Edgar YCor CommunityBot |
Duplicate of Is formula valid for relating $\pi$ with ALL of its OEIS A002485(n)/A002486(n) convergents? | |
| Jun 26, 2022 at 8:49 | comment | added | David Roberts♦ | Link to a pdf of the article @Gerald cited math.ucla.edu/~vsv/resource/general/Lucas.pdf | |
| Jun 26, 2022 at 5:30 | comment | added | Michael Hardy | $355/113$ is not just an "excellent approximation"; it is, like $22/7,$ one of the convergents in the continued fraction representation of $\pi.$ And it differse from $\pi$ by less than the reciprocal of the square of the denominator; thus by less than $1/113^2. \qquad$ | |
| Jun 25, 2022 at 22:11 | review | Close votes | |||
| Jun 26, 2022 at 17:05 | |||||
| Jun 25, 2022 at 20:29 | answer | added | Fetchinson0234 | timeline score: 5 | |
| Jun 25, 2022 at 20:17 | comment | added | Gerald Edgar | @mathworker21 ... that is also quoted at math.stackexchange.com/q/860499/44 | |
| Jun 25, 2022 at 20:13 | comment | added | mathworker21 | My favorite from the paper Gerald linked is $$\frac{355}{113}-\pi = \int_0^1 \frac{x^8(1-x)^8(25+816x^2)}{3164(1+x^2)}dx.$$ | |
| Jun 25, 2022 at 20:08 | comment | added | Gerald Edgar | S.K. Lucas, Integral proofs that $355/113>\pi$, Gazette Aust. Math. Soc. 32 (2005) 263-266. From MathSciNet: "No simple and elegant result was found." | |
| Jun 25, 2022 at 19:34 | history | asked | Pluviophile | CC BY-SA 4.0 |