login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
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

%I #27 Sep 08 2022 08:45:59

%S 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,

%T 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,

%U 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

%N Decimal expansion of arcsin(sqrt(1/3)) and of arccos(sqrt(2/3)).

%C 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

%C 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

%H G. C. Greubel, <a href="/A195695/b195695.txt">Table of n, a(n) for n = 0..5000</a>

%H John D. Barrow, <a href="https://plus.maths.org/content/outer-space">Outer space: Archimedean ice cream cones</a>, +plus magazine.

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Polyhedron">Polyhedron</a>, and further links therein.

%F Also equals arctan(1/sqrt(2)). - _Michel Marcus_, Aug 27 2017

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

%t r = Sqrt[1/3];

%t N[ArcSin[r], 100]

%t RealDigits[%] (* A195695 *)

%t N[ArcCos[r], 100]

%t RealDigits[%] (* A195696 *)

%t N[ArcTan[r], 100]

%t RealDigits[%] (* A019673 *)

%t N[ArcCos[-r], 100]

%t RealDigits[%] (* A195698 *)

%o (PARI) atan(1/sqrt(2)) \\ _Michel Marcus_, Aug 27 2017

%o (Magma) [Arcsin(Sqrt(1/3))]; // _G. C. Greubel_, Nov 18 2017

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

%K nonn,cons

%O 0,1

%A _Clark Kimberling_, Sep 23 2011

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 28 15:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)