A068079 Decimal expansion of 355 / 113.

3, 1, 4, 1, 5, 9, 2, 9, 2, 0, 3, 5, 3, 9, 8, 2, 3, 0, 0, 8, 8, 4, 9, 5, 5, 7, 5, 2, 2, 1, 2, 3, 8, 9, 3, 8, 0, 5, 3, 0, 9, 7, 3, 4, 5, 1, 3, 2, 7, 4, 3, 3, 6, 2, 8, 3, 1, 8, 5, 8, 4, 0, 7, 0, 7, 9, 6, 4, 6, 0, 1, 7, 6, 9, 9, 1, 1, 5, 0, 4, 4, 2, 4, 7, 7, 8, 7, 6, 1, 0, 6, 1, 9, 4, 6, 9, 0, 2, 6, 5, 4, 8, 6, 7, 2, 5, 6, 6, 3, 7, 1, 6, 8, 1, 4, 1, 5, 9, 2

Offset: 1

Author

Nenad Radakovic, Mar 22 2002

Keywords

• easy
• nonn
• cons

Comments

This is an approximation to Pi. It is accurate to 0.00000849%.

355/113 is the third convergent of the continued fraction expansion of Pi (A001203). - Lekraj Beedassy, Jun 18 2003

In one of Ramanujan's papers, a note at the bottom states that "If the area of the circle be 140,000 square miles, then RD [RD = d/2 * Sqrt(355/113) = r*Sqrt(Pi), very nearly] is greater than the true length by about an inch."

This approximation of Pi was suggested by the astronomer Tsu Chúng-chih (A.D. 430 - 501) (see Gullberg). - Stefano Spezia, Jan 13 2025

Examples

			3.141592920353982300884955752212389380530973451327433628318584...
		

References

• Calvin C. Clawson, Mathematical Mysteries, The Beauty and Magic of Numbers, Perseus Books, 1996, p. 88.
• John H. Conway and Richard K. Guy, The Book of Numbers, New York: Springer-Verlag, 1996. See pp. 187, 238-239.
• Jan Gullberg, Mathematics from the Birth of Numbers, W. W. Norton & Co., NY & London, 1997, §3.6 The Quest for Pi, p. 91.
• Ramanujan's papers, "Squaring the circle", Journal of the Indian Mathematical Society, V, 1913, 132. - Robert G. Wilson v, May 30 2014
• David Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, Revised edition 1987. See p. 49.

Links

• Dario Castellanos, The ubiquitous pi, Math. Mag., 61 (1988), 67-98 and 148-163. [_N. J. A. Sloane_, Mar 24 2012]
• Dale, Fun and interesting facts about Pi.
• Index entries for sequences related to the number Pi.
• Index entries for linear recurrences with constant coefficients, signature (1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 1).

Crossrefs

Cf. A068028, A068089, A002485, A002486, A046965, A046947, A083871.

Programs

Maple

Digits:=100: evalf(355/113); # Wesley Ivan Hurt, Mar 14 2015

Mathematica

Flatten[RealDigits[355/113, 10, 100]] (* Wesley Ivan Hurt, Mar 14 2015 *)

PARI

355/113. \\ Charles R Greathouse IV, May 30 2014

PARI

a(n) = if(n==1, 3, digits(16*10^112 \ 113)[(n-2) % 112 + 1]) \\ Jeppe Stig Nielsen, Dec 14 2019

Formula

a(n) = a(n - 112) for n > 113. - Jeppe Stig Nielsen, Dec 14 2019

Extensions

More terms from Sascha Kurz, Mar 23 2002

Terms a(106) and beyond from Jeppe Stig Nielsen, Dec 14 2019