|
|
A339264
|
|
Decimal expansion of (63/25) * (17+15*sqrt(5)) / (7+15*sqrt(5)): an approximation for Pi from Srinivasa Ramanujan.
|
|
0
|
|
|
3, 1, 4, 1, 5, 9, 2, 6, 5, 3, 8, 0, 5, 6, 8, 8, 2, 0, 1, 8, 9, 8, 3, 9, 0, 0, 0, 6, 3, 0, 1, 5, 0, 7, 8, 2, 2, 4, 8, 7, 5, 0, 3, 4, 7, 5, 7, 7, 4, 3, 0, 9, 2, 2, 2, 8, 3, 8, 6, 6, 0, 9, 2, 8, 2, 2, 0, 4, 2, 4, 6, 3, 7, 4, 4, 5, 2, 5, 1, 1, 6, 3, 5, 4, 8, 9, 2, 9, 9, 6
(list;
constant;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
This formula that derives from Ramanujan modular equations is correct to 9 places exactly (see Ramanujan link, page 43).
Pi = 3.1415926535... and this approximation = 3.1415926538...
A quadratic number with minimal polynomial 168125x^2 - 792225x + 829521 and denominator 6725. - Charles R Greathouse IV, Oct 02 2022
|
|
REFERENCES
|
Jörg Arndt and Christoph Haenel, Pi Unleashed, Springer-Verlag, 2006, retrieved Jun 05 2013, (4.17) page 57.
David Wells, The Penguin Dictionary of Curious and Interesting Numbers (Revised Edition), Penguin Books, 1997, entry 3.14159 (Pi), page 36.
|
|
LINKS
|
|
|
FORMULA
|
Equals (63/13450) * (503+75*sqrt(5)).
Equals the root of 829521 - 792225*x + 168125*x^2 which is > 3. - Peter Luschny, Nov 29 2020
|
|
EXAMPLE
|
3.141592653805688201898390006301507822487503475774...
|
|
MAPLE
|
evalf((63/25)*(17+15*sqrt(5))/(7+15*sqrt(5)), 100);
|
|
MATHEMATICA
|
RealDigits[(63/25)*(17 + 15*Sqrt[5])/(7 + 15*Sqrt[5]), 10, 100][[1]] (* Amiram Eldar, Nov 29 2020 *)
|
|
PROG
|
(PARI) (63/13450) * (503+75*sqrt(5)) \\ Michel Marcus, Nov 29 2020
|
|
CROSSREFS
|
|
|
KEYWORD
|
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|