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nextstep

Joined: 06 Jan 2007
Posts: 539

Posted: Wed Sep 10, 2014 2:19 am    Post subject: Henneberg's Minimal Surface (deg 15)

Hi all,
In differential geometry, the Henneberg surface is a non-orientable minimal surface named after Lebrecht Henneberg (1850-1933).
It's a minimal surface and double algebraic surface of 15th order and fifth class which can be given by parametric equations

x(u,v) = 2sinhucosv-2/3sinh(3u)cos(3v)
y(u,v) = 2sinhusinv+2/3sinh(3u)sin(3v)
z(u,v) = 2cosh(2u)cos(2v)

Up until 1981 it was the only known non-orientable minimal surface.
 Code: {     "Param3D": {         "Component": [             "Henneberg"         ],         "Description": [             "Description of the model"         ],         "Fx": [             "2*sinh(u)*cos(v)-(2/3)*sinh(3*u)*cos(3*v)"         ],         "Fy": [             "2*sinh(u)*sin(v)+(2/3)*sinh(3*u)*sin(3*v)"         ],         "Fz": [             "2*cosh(2*u)*cos(2*v)"         ],         "Name": [             "Henneberg"         ],         "Umax": [             "1"         ],         "Umin": [             "-1"         ],         "Vmax": [             "pi/2"         ],         "Vmin": [             "-pi/2"         ]     } }

Henneberg by taha_ab, on Flickr
_________________
Cheers,
Abderrahman
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