A210621 - OEIS

%I #47 Jan 12 2025 03:50:16

%S 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,

%T 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,

%U 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

%N Decimal expansion of 256/81.

%C 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

%D Petr Beckmann, A History of Pi, 3rd Ed., Boulder, Colorado: The Golem Press (1974): p. 12.

%D Calvin C. Clawson, Mathematical Mysteries, The Beauty and Magic of Numbers, Perseus Books, 1996, p. 88.

%D Jan Gullberg, Mathematics from the Birth of Numbers, W. W. Norton & Co., NY & London, 1997, §3.6 The Quest for Pi, p. 89.

%D Carl Theodore Heisel, Behold! The grand problem no longer unsolved: The circle squared beyond refutation, c. 1935. (proposes Pi = 3 + 13/81)

%D Eli Maor, e: The Story of a Number. Princeton, New Jersey: Princeton University Press (1994): 41, 47 note 1.

%D David Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, Revised edition 1987. See p. 48.

%H Dario Castellanos, <a href="http://www.jstor.org/stable/2690037">The ubiquitous Pi</a>, Math. Mag., 61 (1988), 67-98 and 148-163.

%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,1).

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

%F Equals 3*A229943 = A255910^2 = A268315/3. - _Hugo Pfoertner_, Jun 26 2024

%e 3.1604938271604938271604938271604938271604938271604938271604...

%t RealDigits[256/81, 10, 100][[1]] (* _Alonso del Arte_, Jun 12 2012 *)

%o (PARI) 256/81. \\ _Charles R Greathouse IV_, Sep 13 2013

%Y Cf. A068028, A229943, A255910, A268315.

%K nonn,cons,easy

%O 1,1

%A _N. J. A. Sloane_, Mar 24 2012

%E Offset corrected by _Rick L. Shepherd_, Jan 06 2014