login
This site is supported by donations to The OEIS Foundation.

 

Logo

Annual appeal: Please make a donation to keep the OEIS running! Over 6000 articles have referenced us, often saying "we discovered this result with the help of the OEIS".
Other ways to donate

Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A195695 Decimal expansion of arcsin(sqrt(1/3)) and of arccos(sqrt(2/3)). 7
6, 1, 5, 4, 7, 9, 7, 0, 8, 6, 7, 0, 3, 8, 7, 3, 4, 1, 0, 6, 7, 4, 6, 4, 5, 8, 9, 1, 2, 3, 9, 9, 3, 6, 8, 7, 8, 5, 5, 1, 7, 0, 0, 0, 4, 6, 7, 7, 5, 4, 7, 4, 1, 9, 5, 2, 7, 7, 7, 4, 1, 6, 6, 8, 3, 1, 9, 9, 6, 1, 5, 7, 2, 3, 9, 1, 2, 8, 0, 4, 3, 9, 2, 6, 6, 2, 5, 8, 1, 0, 0, 8, 5, 4, 3, 0, 4, 6, 0, 5 (list; constant; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

The complementary magic angle, that is, Pi/2 - A195696. The angle between the body-diagonal and a congruent face-diagonal of a cube. And also the polar angle of the cone circumscribed to a regular tetrahedron from one of its vertices. - Stanislav Sykora, Nov 21 2013

This is the value of the angle of the circular cone to the axis, that maximizes the volume of the cone enclosed by a given area. See the +plus link. - Michel Marcus, Aug 27 2017

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..5000

John D. Barrow, Outer space: Archimedean ice cream cones, +plus magazine.

Wikipedia, Polyhedron, and further links therein.

FORMULA

Also equals arctan(1/sqrt(2)). - Michel Marcus, Aug 27 2017

EXAMPLE

arcsin(sqrt(1/3)) = 0.61547970867038734106746458912399...

MATHEMATICA

r = Sqrt[1/3];

N[ArcSin[r], 100]

RealDigits[%]  (* A195695 *)

N[ArcCos[r], 100]

RealDigits[%]  (* A195696 *)

N[ArcTan[r], 100]

RealDigits[%]  (* A019673 *)

N[ArcCos[-r], 100]

RealDigits[%]  (* A195698 *)

PROG

(PARI) atan(1/sqrt(2)) \\ Michel Marcus, Aug 27 2017

(MAGMA) [Arcsin(Sqrt(1/3))]; // G. C. Greubel, Nov 18 2017

CROSSREFS

Cf. A195696 (magic angle), A195698, A020760, A157697, A243445.

Sequence in context: A212006 A245725 A011096 * A199047 A021623 A197296

Adjacent sequences:  A195692 A195693 A195694 * A195696 A195697 A195698

KEYWORD

nonn,cons

AUTHOR

Clark Kimberling, Sep 23 2011

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent | More pages
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy .

Last modified December 16 11:52 EST 2017. Contains 296087 sequences.