A193373 -id:A193373 - cp's OEIS frontend

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

Offset: 0

Frank M Jackson, Jul 24 2011

This is the first of the three angles (in radians) of a unique triangle that is right angled and where the angles are in a harmonic progression: Pi/(2+2*sqrt(2)) (this sequence), Pi/(2+sqrt(2)) (A193373), Pi/2 (A019669). The angles (in degrees) are approximately 37.279, 52.721, 90. The common difference between the denominators of the harmonic progression is sqrt(2).

			0.6506451422...

G. C. Greubel, Table of n, a(n) for n = 0..10000
Index entries for transcendental numbers

SetDefaultRealField(RealField(100)); R:= RealField(); Pi(R)/(2 + 2*Sqrt(2)); // G. C. Greubel, Sep 29 2018

evalf(Pi/(2+2*sqrt(2)),120); # Muniru A Asiru, Sep 30 2018

N[Pi/(2 + 2*Sqrt[2]), 100]
RealDigits[Pi/(2 + 2*Sqrt[2]), 10, 100][[1]] (* G. C. Greubel, Sep 29 2018 *)

default(realprecision,100); Pi/(2+2*sqrt(2))

Equals Pi/(2+2*sqrt(2)).
Equals Integral_{x=0..Pi/2} cos(x)^2/(1 + sin(x)^2) dx = Integral_{x=0..Pi/2} sin(x)^2/(1 + cos(x)^2) dx. - Amiram Eldar, Aug 16 2020
Equals 4*Sum_{k >= 0} (-1)^k/((4*k + 1)*(4*k + 2)*(4*k + 3)). - Peter Bala, Jul 15 2024
Equals Integral_{x=0..1} sqrt(1 - x^2)/(1 + x^2) dx. - Kritsada Moomuang, Jun 05 2025
Equals A247719 - A019669 = A000796*A268683. - R. J. Mathar, Jul 22 2025

cp's OEIS Frontend

A193355 Decimal expansion of Pi/(2 + 2*sqrt(2)).

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