A127454 - OEIS

%I #20 Jul 04 2014 12:52:39

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

%T 3,7,0,0,9,6,7,2,5,3,0,9,7,6,2,4,4,3,7,6,9,5,8,3,5,3,0,9,9,2,2,4,6,3,

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

%N Decimal expansion of transcendental solution to round pegs in square holes problem.

%C This value "must be determined numerically. As a result, a round peg fits better into a square hole than a square peg fits into a round hole only for integer dimensions n < 9."

%H Robert G. Wilson v, <a href="/A127454/b127454.txt">Table of n, a(n) for n = 1..1001</a>

%H David Singmaster, <a href="http://www.jstor.org/stable/2689251">On Round Pegs in Square Holes and Square Pegs in Round Holes</a>, Math. Mag. 37, 335-339, 1964.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Peg.html">Peg.</a>

%F Where the real number ratio crosses 1 in (Pi^n)(n^(n/2))/(2^(2n))(Gamma(1+n/2))^2. n such that (Pi^n)(n^(n/2)) = (2^(2n))(Gamma(1+n/2))^2.

%e 8.13794104609137237652983898405322337009672530976244376958353099224630941205660...

%t RealDigits[ FindRoot[ Pi^x*x^(x/2) == 2^(2 x) Gamma[1 + x/2]^2, {x, 8}, WorkingPrecision -> 121][[1, 2]], 10, 111][[1]] (* _Robert G. Wilson v_, Jul 03 2014 *)

%Y Cf. A194940.

%K cons,nonn

%O 1,1

%A _Jonathan Vos Post_, Jan 13 2007

%E More terms from _Eric W. Weisstein_, Jan 15 2007