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Bour's surface crosses itself on three coplanar rays, meeting at equal angles at the origin of the space. The rays partition the surface into six sheets, topologically equivalent to half-planes; three sheets lie in the halfspace above the plane of the rays, and three below. Four of the sheets are
365:{\displaystyle {\begin{aligned}x(r,\theta )&=r\cos(\theta )-{\tfrac {1}{2}}r^{2}\cos(2\theta )\\y(r,\theta )&=-r\sin(\theta )(r\cos(\theta )+1)\\z(r,\theta )&={\tfrac {4}{3}}r^{3/2}\cos \left({\tfrac {3}{2}}\theta \right).\end{aligned}}}
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Ulrich
Dierkes, Stefan Hildebrandt, Friedrich Sauvigny, Minimal Surfaces, Volume 1. Springer 2010
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The surface can also be expressed as the solution to a polynomial equation of order 16 in the
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Weisstein, Eric W. "Bour's
Minimal Surface." From MathWorld--A Wolfram Web Resource.
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into minimal surfaces, produces this surface for the two functions
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479:Robertson, Edmund F.
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454:developable
56:Description
50:Edmond Bour
464:References
380:Properties
639:Riemann's
611:Henneberg
576:Catalan's
348:θ
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282:θ
251:θ
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230:θ
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215:−
202:θ
180:θ
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143:−
137:θ
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112:θ
683:Category
634:Richmond
624:Lidinoid
606:Helicoid
581:Catenoid
65:Equation
654:Schwarz
629:Neovius
596:Enneper
591:Costa's
456:onto a
649:Scherk
601:Gyroid
571:Bour's
619:-noid
384:The
325:cos
242:cos
221:sin
168:cos
128:cos
685::
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