%I #25 Jul 30 2018 14:55:41

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

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

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

%N Decimal expansion of arctan(2*Pi): adjacent angle for a right triangle of equal area to a disk.

%C In radians, this constant is the arctan(base / height) = arctan(Adjacent / Opposite) = arctan(circumference / radius) for a unit circle is arctan(A019692), where A019692 = 2*A000796.

%C "Archimedes used the tools of Euclidean geometry to show that the area inside a circle is equal to that of a right triangle whose base has the length of the circle's circumference and whose height equals the circle's radius in his book Measurement of a Circle." quote from Wikipedia link.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Area_of_a_circle#Triangle_proof">Area of a circle: Triangle proof</a>

%F Equals A019669 - A233527. [_Bruno Berselli_, Dec 16 2013]

%e 1.412965136506737759063712949856932518493513459088501850071914328940...

%t RealDigits[ArcTan[2 Pi], 10, 110][[1]] (* _Bruno Berselli_, Dec 16 2013 *)

%o (PARI) atan(2*Pi)

%Y Cf. A019692: 2*Pi; A232273: arctan(Pi); A233527: arctan(1/(2*Pi)).

%K nonn,cons

%O 1,2

%A _John W. Nicholson_, Dec 11 2013