cp's OEIS Frontend

A195695 Decimal expansion of arcsin(sqrt(1/3)) and of arccos(sqrt(2/3)).

%I A195695 #29 Nov 21 2024 07:40:51
%S A195695 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 A195695 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 A195695 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 A195695 Decimal expansion of arcsin(sqrt(1/3)) and of arccos(sqrt(2/3)).
%C A195695 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 A195695 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 A195695 G. C. Greubel, <a href="/A195695/b195695.txt">Table of n, a(n) for n = 0..5000</a>
%H A195695 John D. Barrow, <a href="https://plus.maths.org/content/outer-space">Outer space: Archimedean ice cream cones</a>, +plus magazine.
%H A195695 Wikipedia, <a href="http://en.wikipedia.org/wiki/Polyhedron">Polyhedron</a>, and further links therein.
%H A195695 <a href="/index/Tra#transcendental">Index entries for transcendental numbers</a>
%F A195695 Also equals arctan(1/sqrt(2)). - _Michel Marcus_, Aug 27 2017
%e A195695 arcsin(sqrt(1/3)) = 0.61547970867038734106746458912399...
%t A195695 r = Sqrt[1/3];
%t A195695 N[ArcSin[r], 100]
%t A195695 RealDigits[%]  (* A195695 *)
%t A195695 N[ArcCos[r], 100]
%t A195695 RealDigits[%]  (* A195696 *)
%t A195695 N[ArcTan[r], 100]
%t A195695 RealDigits[%]  (* A019673 *)
%t A195695 N[ArcCos[-r], 100]
%t A195695 RealDigits[%]  (* A195698 *)
%o A195695 (PARI) atan(1/sqrt(2)) \\ _Michel Marcus_, Aug 27 2017
%o A195695 (Magma) [Arcsin(Sqrt(1/3))]; // _G. C. Greubel_, Nov 18 2017
%Y A195695 Cf. A195696 (magic angle), A195698, A020760, A157697, A243445.
%K A195695 nonn,cons
%O A195695 0,1
%A A195695 _Clark Kimberling_, Sep 23 2011