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A338004
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Decimal expansion of the angle of association yielding the gyroid relative to Schwarz's D surface.
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0
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6, 6, 3, 4, 8, 2, 9, 7, 0, 5, 1, 1, 4, 3, 4, 8, 0, 8, 0, 5, 7, 5, 6, 8, 8, 4, 7, 4, 3, 7, 2, 3, 9, 9, 5, 0, 0, 0, 5, 0, 4, 2, 8, 9, 8, 5, 1, 5, 6, 9, 6, 2, 5, 5, 4, 5, 7, 1, 8, 2, 4, 4, 9, 9, 5, 0, 5, 9, 3, 3, 1, 5, 0, 9, 3, 7, 7, 6, 8, 3, 8, 5, 0, 6, 8, 1, 0, 9, 7, 9, 1, 5, 6, 8, 7, 8, 5, 8, 9, 8, 7, 3, 3, 3, 0, 1, 0, 9, 0, 8, 3, 3, 8, 9, 1, 3, 9, 4, 5, 4
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OFFSET
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0,1
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COMMENTS
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For every minimal surface, an associate family of minimal surfaces can be defined by adding an angle of association to the base surface's Weierstrass-Enneper parametrization.
If the base is Schwarz's D surface, an angle of association of Pi/2 yields Schwarz's P surface; this entry is the only other angle for which the resulting associate surface - the gyroid - is embedded.
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LINKS
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FORMULA
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Equals arctan(K(1/4) / K(3/4)), where K is the complete elliptic integral of the first kind.
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EXAMPLE
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0.66348297051143480805756884743723...
In degrees: 38.0147739891080681076130861019883...
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MATHEMATICA
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First@ RealDigits@ N[ArcTan[EllipticK[1/4] / EllipticK[3/4]], 120]
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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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