OFFSET
1,1
COMMENTS
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."
LINKS
Robert G. Wilson v, Table of n, a(n) for n = 1..1001
David Singmaster, On Round Pegs in Square Holes and Square Pegs in Round Holes, Math. Mag. 37, 335-339, 1964.
Eric Weisstein's World of Mathematics, Peg.
FORMULA
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.
EXAMPLE
8.13794104609137237652983898405322337009672530976244376958353099224630941205660...
MATHEMATICA
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 *)
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
Jonathan Vos Post, Jan 13 2007
EXTENSIONS
More terms from Eric W. Weisstein, Jan 15 2007
STATUS
approved