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Serie V, Nr 7b

The envelope of the geodesic lines on the ellipsoid, coming from one point. Spheroid, with the envelope for two different starting points.


Mathematical description
The model represents an prolate ellipsoid of revolution, i.e., a surface generated by rotating an ellipse about its major axis. The ellipsoid is given by the equation:

                  y2    x2+z2
                ---- + -----  = 1,
                (ac)2    a2
with c2<1.
There is an envelope of a family of curves on the ellipsoid. The envelope surface is a surface touching every member of the family. The family of curves considered in this model are the geodesic lines on the ellipsoid. A geodesic is a locally lenght minimizing curve.

Title model and translation
Die Enveloppen der von einem Punkt ausgehenden geodätischen Linien auf dem Rotationsellipsoid. Das Sphäroid, mit den Enveloppen für zwei verschiedene Ausgangspunkte.
The envelope of the geodesic lines on the ellipsoid, coming from one point. Spheroid, with the envelope for two different starting points.

Text on Sticker and translation
Enveloppe geodätischer linien.
The envelope of the geodesic lines.

Designer
Dr. A. v. Braunmühl under the supervision of Dr. A. Brill
München in 1880

Company
Martin Schilling in Halle a.S.

Original price
Mark 7,50

Dimension
7-10 cm

Material
Plaster

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