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A137218 Decimal expansion of the argument of -1 + 2*i. 10

%I

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

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

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

%N Decimal expansion of the argument of -1 + 2*i.

%C Gives closed forms for many arctangent values:

%C arctan(2) = Pi - a, arctan(1/2) = a - Pi/2,

%C arctan(3) = a - Pi/4, arctan(1/3) = 3*Pi/4 - a,

%C arctan(7) = 7*Pi/4 - 2*a, arctan(1/7) = 2*a - 5*Pi/4,

%C arctan(4/3) = 2*a - Pi and arctan(3/4) = 3*Pi/2 - 2*a.

%C Dihedral angle in the dodecahedron (radians). - _R. J. Mathar_, Mar 24 2012

%C Larger interior angle (in radians) of a golden rhombus; A105199 is the smaller interior angle. - _Eric W. Weisstein_, Dec 17 2018

%H Rick L. Shepherd, <a href="/A137218/b137218.txt">Table of n, a(n) for n = 1..20000</a>

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

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Dodecahedron">Dodecahedron</a>

%F Equals Pi - arctan(2) = A000796 - A105199 = 2*A195723.

%e 2.0344439357957027354455779231...

%t RealDigits[Pi - ArcTan[2], 10, 120][[1]] (* _Harvey P. Dale_, Aug 08 2014 *)

%o (PARI)

%o default(realprecision, 120);

%o acos(-1/sqrt(5)) \\ or

%o arg(-1+2*I) \\ _Rick L. Shepherd_, Jan 26 2014

%Y Platonic solids' dihedral angles: A137914 (tetrahedron), A156546 (octahedron), A019669 (cube), A236367 (icosahedron). - _Stanislav Sykora_, Jan 23 2014

%Y Cf. A242723 (same in degrees).

%Y Cf. A105199 (smaller interior angle of the golden rhombus).

%K cons,nonn

%O 1,1

%A Matt Rieckman (mjr162006(AT)yahoo.com), Mar 06 2008

%E Corrected a typo in the sequence Matt Rieckman (mjr162006(AT)yahoo.com), Feb 05 2010

%E More terms from _Rick L. Shepherd_, Jan 26 2014

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Last modified March 31 03:08 EDT 2020. Contains 333136 sequences. (Running on oeis4.)