OFFSET
0,1
COMMENTS
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.
LINKS
A. Schoen, Infinite Periodic Minimal Surfaces Without Self-Intersections, NASA Technical Note D-5541, 1970.
A. Schoen, Triply-periodic minimal surfaces
Wikipedia, Associate family
FORMULA
Equals arctan(K(1/4) / K(3/4)), where K is the complete elliptic integral of the first kind.
EXAMPLE
0.66348297051143480805756884743723...
In degrees: 38.0147739891080681076130861019883...
MATHEMATICA
First@ RealDigits@ N[ArcTan[EllipticK[1/4] / EllipticK[3/4]], 120]
CROSSREFS
KEYWORD
nonn,cons
AUTHOR
Jeremy Tan, Oct 06 2020
STATUS
approved