

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
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OFFSET

0,1


COMMENTS

The complementary magic angle, that is, Pi/2  A195696. The angle between the bodydiagonal and a congruent facediagonal 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



