Henneberg's Minimal Surface (deg 15)

 
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nextstep
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PostPosted: Wed Sep 10, 2014 2:19 am    Post subject: Henneberg's Minimal Surface (deg 15) Reply with quote

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
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Abderrahman
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