A233528 Decimal expansion of arctan(2*Pi): adjacent angle for a right triangle of equal area to a disk.

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, 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, 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

Offset

1,2

Comments

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.

"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.

Links

Table of n, a(n) for n=1..100.

Wikipedia, Area of a circle: Triangle proof

Formula

Equals A019669 - A233527. [Bruno Berselli, Dec 16 2013]

Example

1.412965136506737759063712949856932518493513459088501850071914328940...

Mathematica

RealDigits[ArcTan[2 Pi], 10, 110][[1]] (* Bruno Berselli, Dec 16 2013 *)

Prog

(PARI) atan(2*Pi)

Crossrefs

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

Sequence in context: A331152 A264922 A341030 * A084604 A152253 A280440

Adjacent sequences: A233525 A233526 A233527 * A233529 A233530 A233531

Keyword

nonn,cons

Author

John W. Nicholson, Dec 11 2013

Status

approved