OFFSET
0,2
COMMENTS
Decimal expansion of the real number quantifying the area of the Apollonian gasket of three congruent circles of radius 1.
General solution: This constant is the ratio of r^2, where r is the radius of three congruent circles forming a Apollonian gasket, to the area of that Apollonian gasket.
sqrt(3)-pi/2 is the area enclosed between three identical osculating circles of unit radius. - Lekraj Beedassy, Apr 12 2006
LINKS
Eric Weisstein's World of Mathematics, Apollonian Gasket.
FORMULA
a(n) = 3^(1/2) - pi/2.
EXAMPLE
0.16125448077398067429612464986612...
RealDigits[ Sqrt[3] - Pi/2, 10, 105][[1]]
MATHEMATICA
RealDigits[N[Sqrt[3] - Pi/2, 300]][[1]] (* Vladimir Joseph Stephan Orlovsky, Jul 03 2011 *)
PROG
(PARI) sqrt(3)-Pi/2 \\ Charles R Greathouse IV, Oct 01 2022
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
Christopher M. Tomaszewski (cmt1288(AT)comcast.net), Feb 01 2004
EXTENSIONS
More terms from Robert G. Wilson v, Feb 09 2004
Edited by N. J. A. Sloane, Jul 05 2008 at the suggestion of Rick L. Shepherd
STATUS
approved