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A235509
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Decimal expansion of arccos(4/5).
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2
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6, 4, 3, 5, 0, 1, 1, 0, 8, 7, 9, 3, 2, 8, 4, 3, 8, 6, 8, 0, 2, 8, 0, 9, 2, 2, 8, 7, 1, 7, 3, 2, 2, 6, 3, 8, 0, 4, 1, 5, 1, 0, 5, 9, 1, 1, 1, 5, 3, 1, 2, 3, 8, 2, 8, 6, 5, 6, 0, 6, 1, 1, 8, 7, 1, 3, 5, 1, 2, 4, 7, 4, 8, 1, 1, 6, 2, 1, 0, 8, 8, 7, 1, 2, 8, 1, 6, 8, 4, 4, 7, 0, 1, 2, 8, 2, 7, 4, 8, 8
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OFFSET
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0,1
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COMMENTS
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Given a square ABCD, there is one point M equidistant from A, B and the middle of CD. The measure of the angle BAM is arccos(4/5) (or arcsec(5/4)). This angle is the smallest angle of the well-known (3, 4, 5) Pythagorean triangle.
Also the polar angle phi of the viewing cone that cuts out exactly 10% of the celestial sphere; phi = arccos(1-2f), where f is the cut-out fraction of the full solid angle. - Stanislav Sykora, Feb 14 2016
Given a triangle ABC whose medians drawn from A and B are perpendicular in centroid G, then angle C <= arccos(4/5) (see Maths Challenge link with figure and proof). - Bernard Schott, Mar 29 2023
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LINKS
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FORMULA
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EXAMPLE
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0.64350110879328438680280922871732263804151059111531238286560611871351...
In degrees: 36.869897645844...°
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MATHEMATICA
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RealDigits[ArcCos[4/5], 10, 100] // First
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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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