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A195695
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Decimal expansion of arcsin(sqrt(1/3)) and of arccos(sqrt(2/3)).
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7
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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
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0,1
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COMMENTS
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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
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LINKS
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FORMULA
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EXAMPLE
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arcsin(sqrt(1/3)) = 0.61547970867038734106746458912399...
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MATHEMATICA
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r = Sqrt[1/3];
N[ArcSin[r], 100]
N[ArcCos[r], 100]
N[ArcTan[r], 100]
N[ArcCos[-r], 100]
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PROG
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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