OFFSET
1,1
COMMENTS
Gives closed forms for many arctangent values:
arctan(2) = Pi - a, arctan(1/2) = a - Pi/2,
arctan(3) = a - Pi/4, arctan(1/3) = 3*Pi/4 - a,
arctan(7) = 7*Pi/4 - 2*a, arctan(1/7) = 2*a - 5*Pi/4,
arctan(4/3) = 2*a - Pi and arctan(3/4) = 3*Pi/2 - 2*a.
Dihedral angle in the dodecahedron (radians). - R. J. Mathar, Mar 24 2012
Larger interior angle (in radians) of a golden rhombus; A105199 is the smaller interior angle. - Eric W. Weisstein, Dec 17 2018
LINKS
Rick L. Shepherd, Table of n, a(n) for n = 1..20000
Eric Weisstein's World of Mathematics, Golden Rhombus
Wikipedia, Dodecahedron
EXAMPLE
2.0344439357957027354455779231...
MATHEMATICA
RealDigits[Pi - ArcTan[2], 10, 120][[1]] (* Harvey P. Dale, Aug 08 2014 *)
PROG
(PARI)
default(realprecision, 120);
acos(-1/sqrt(5)) \\ or
arg(-1+2*I) \\ Rick L. Shepherd, Jan 26 2014
CROSSREFS
KEYWORD
cons,nonn
AUTHOR
Matt Rieckman (mjr162006(AT)yahoo.com), Mar 06 2008
EXTENSIONS
Corrected a typo in the sequence Matt Rieckman (mjr162006(AT)yahoo.com), Feb 05 2010
More terms from Rick L. Shepherd, Jan 26 2014
STATUS
approved