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Serie VI, Nr 4

The wave surface for optical biaxial crystal in individual octant with the spherical and ellipsoid lines.


Mathematical description
The model represents a wave surface for optical two-axis crystal in particular octants. The surface is created by the following ellipsoid and his complement:

                 x2    y2    z2
                --- + --- + ---  = 1
                 a2    b2    c2
It has spherical and ellipsoidic lines on it. Four octants have a hole on the outside shell (umbilical point), given by the equation:
                 x4      b3    a-c
                ---  =  --- × ----
                 y4      a3    b-c
The other four octants have a hole on the inside shell, given by the equation:
                 z4      b3    a-c
                ---  =  --- × ----
                 y4      c3    a-b

Title model and translation
Die Wellenfläche für optisch zweiaxige Krystalle in einzelnen Octanten mit den sphärischen und ellipsoidischen Lininen auf beiden Mänteln und 8 Nabelpunkten.
The wave surface for optical biaxial crystal in individual octant with the spherical and ellipsoid lines.

Text on Sticker and translation
Fresnel'sche Wellenfl. mit spär linien.
Fresnel's wave surface with spherical lines.

Designer
Herrn Rector Dr. Böklen
München in 1880

Company
L. Brill in Darmstadt

Original price
Mark 10,-

Dimension
24-9 cm

Material
Plaster

Literature
Schilling, M., Catalog mathematischer Modelle für den höheren mathematischen Unterricht, Leipzig: Verlag von Martin Schilling, 1911