A120671 -id:A120671 - cp's OEIS frontend

A120669 Decimal expansion of arccos(1-8/(Pi^2)).

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

Offset: 1

Rick L. Shepherd, Jun 22 2006

For a circle with radius r, the measurement in radians of the central angle with endpoints on the circle that are r*4/Pi apart: The average central angle (<= Pi) formed using two randomly chosen points on a circle. The average arc length between such endpoints is r*A120669 corresponding to the average chord length r*A088538; so for the unit circle arc length is A120669 and chord length is A088538.

			1.38021418274907990400875581814...

Cf. A088538, A120670 (same in degrees), A120671 (A120669/2Pi).

RealDigits[ArcCos[1-8/Pi^2],10,120][[1]] (* Harvey P. Dale, Dec 15 2014 *)

PARI
```
acos(1-8/Pi^2)
```

A120670 Decimal expansion of 180*arccos(1-8/(Pi^2))/Pi.

Original entry on oeis.org

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

Offset: 2

Rick L. Shepherd, Jun 22 2006

For a circle with radius r, the measurement in degrees of the central angle with endpoints on the circle that are r*4/Pi apart: The average central angle (<= 180 degrees) formed using two randomly chosen points on a circle. The average arc length between such endpoints is r*A120669 corresponding to the average chord length r*A088538; so for the unit circle arc length is A120669 and chord length is A088538.

			79.0804474956203908253980311180...

Cf. A088538, A120669 (same in radians), A120671 (A120670/360).

RealDigits[180 ArcCos[1-8/Pi^2]/Pi,10,120][[1]] (* Harvey P. Dale, Feb 17 2023 *)

PARI
```
180*acos(1-8/Pi^2)/Pi
```

Equals 180*A120669/Pi = 360*A120671.

cp's OEIS Frontend

A120669 Decimal expansion of arccos(1-8/(Pi^2)).

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