A232247 -id:A232247 - cp's OEIS frontend

A232182 Decimal expansion of the arctan of Pi/2.

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

Offset: 1

R. J. Mathar, Nov 20 2013

			Equals 1.00388482185388721414842394491713228829210446059487057472971...

Cf. A019669, A232247.

Maple
```
evalf(arctan(Pi/2)) ;
```

RealDigits[ArcTan[Pi/2],10,120][[1]] (* Harvey P. Dale, Jan 31 2015 *)

Equals A019669 - A232247. [Bruno Berselli, Nov 20 2013]

A232272 Decimal expansion of arctan(1/Pi).

Original entry on oeis.org

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

Offset: 0

Bruno Berselli, Nov 22 2013

			0.30816907111598493578699960803405309858963702926316931351366234390168...

Jerome Spanier and Keith B. Oldham, "Atlas of Functions", Hemisphere Publishing Corp., 1987, chapter 35, page 338.

Cf. A019669, A049541, A232247, A232273.

Mathematica
```
RealDigits[ArcTan[1/Pi], 10, 90][[1]]
```

atan(1/Pi) \\ Charles R Greathouse IV, Nov 26 2024

Equals A019669 - A232273.
Equals Sum_{i>=0} (-1)^k/((1+2*k)*Pi^(1+2*k)).
From Wolfe Padawer, Feb 16 2023: (Start)
Equals arccot(Pi).
Equals arcsin(1/sqrt(Pi^2 + 1)).
Equals arccos(1/sqrt(1 + 1/Pi^2)). (End)

A275477 Decimal expansion of arccos(2/Pi).

Original entry on oeis.org

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

Offset: 0

Jeremy Tan, Jul 29 2016

The Winkel tripel projection is the average of the Aitoff projection and an equirectangular projection. The latter component depends on a standard parallel which in radians is this constant.

			0.88068923542035666722694378256890...

Mike Bostock, Winkel Tripel
Wikipedia, Winkel tripel projection

Cf. A060294 (2/Pi), A232247 (arctan(2/Pi)).

First@ RealDigits@ N[ArcCos[2/Pi], 120] (* Michael De Vlieger, Aug 06 2016 *)

PARI
```
acos(2/Pi)
```

A317704 Decimal expansion of arctan(2/Pi)*180/Pi.

Original entry on oeis.org

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

Offset: 2

Seiichi Manyama, Aug 04 2018

The degree of the slope when spreading books. The binding and cover are such that each of the pages follows a quarter-circle arc that begins at the binding and intersects it perpendicularly, and that the length of the arc for the last (or first) page of the book is zero.
   _____
   =======\
   ========\

			32.481636590529753597442716152734642...

Cf. A232247 (arctan(2/Pi)).

RealDigits[ArcTan[2/Pi]*180/Pi, 10, 100][[1]] (* Amiram Eldar, Jun 26 2021 *)

PARI
```
atan(2/Pi)*180/Pi
```

More terms from Jon E. Schoenfield, Aug 05 2018

A331480 Decimal expansion of arcsin(2/Pi).

Original entry on oeis.org

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

Offset: 0

Jianing Song, Jan 18 2020

			0.69010709137453995200...

Cf. A060294 (decimal expansion of 2/Pi), A275477 (arccos(2/Pi)), A232247 (arctan(2/Pi)), A232182 (arccot(2/Pi)).

Mathematica
```
First@RealDigits@N[ArcSin[2/Pi], 120]
```
PARI
```
default(realprecision, 100); asin(2/Pi)
```

Equals Pi/2 - A275477.

cp's OEIS Frontend

A232182 Decimal expansion of the arctan of Pi/2.

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A232272 Decimal expansion of arctan(1/Pi).

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A275477 Decimal expansion of arccos(2/Pi).

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A317704 Decimal expansion of arctan(2/Pi)*180/Pi.

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Extensions

A331480 Decimal expansion of arcsin(2/Pi).

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