A210621 Decimal expansion of 256/81.

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

Offset: 1

Author

N. J. A. Sloane, Mar 24 2012

Keywords

• nonn
• cons
• easy

Comments

According to Maor (1994), the Rhind Papyrus asserts that a circle has the same area as a square with a side that is 8/9 the diameter of the circle. From this we can determine that 256/81 is one of the ancient Egyptian approximations of Pi. - Alonso del Arte, Jun 12 2012

Examples

			3.1604938271604938271604938271604938271604938271604938271604...
		

References

• Petr Beckmann, A History of Pi, 3rd Ed., Boulder, Colorado: The Golem Press (1974): p. 12.
• 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 p. 237.
• Jan Gullberg, Mathematics from the Birth of Numbers, W. W. Norton & Co., NY & London, 1997, §3.6 The Quest for Pi, p. 89.
• Carl Theodore Heisel, Behold! The grand problem no longer unsolved: The circle squared beyond refutation, c. 1935. (proposes Pi = 3 + 13/81)
• Eli Maor, e: The Story of a Number. Princeton, New Jersey: Princeton University Press (1994): 41, 47 note 1.
• David Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, Revised edition 1987. See p. 48.

Links

• Dario Castellanos, The ubiquitous Pi, Math. Mag., 61 (1988), 67-98 and 148-163.
• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,1).

Crossrefs

Cf. A068028, A229943, A255910, A268315.

Programs

Mathematica

RealDigits[256/81, 10, 100][[1]] (* Alonso del Arte, Jun 12 2012 *)

PARI

256/81. \\ Charles R Greathouse IV, Sep 13 2013

Formula

256/81 = (4/3)^4.

Equals 3*A229943 = A255910^2 = A268315/3. - Hugo Pfoertner, Jun 26 2024

Extensions

Offset corrected by Rick L. Shepherd, Jan 06 2014