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Serie I, Nr 3b

The enveloping surface of a system of rays of a one sheet hyperboloid. The two components are associated.


  

Mathematical description
An one sheeted hyperboloid is a surface of revolution obtained by rotating a hyperbola about the perpendicular bisector of the line between its foci. This model is from geometrical optics. Parallel rays of light are reflected in the one sheeted hyperboloid, whose equation is:

                 x2     y2     z2
                --- + --- — ---  = 1
                 52     22     12
The models show the surfaces S which are enveloped by all these reflected rays. This surface are described by the following:
S = { (x,y,z) | ∃v 20y2=(v-5/2)3(3v+5/2+x2/25) }
-5z2=(v+5/2)3(3v-5/2+x2/25)
The surface has two components that are associated in the model.

Title model and translation
Die Geodätischen Linien auf dem Rotationsellipsoid.
The enveloping surface of a system of rays of a one sheet hyperboloid. The two components are associated.

Text on Sticker and translation
Centrafläche des hyperboloids.
The enveloping surface of a system of rays of a hyperboloid.

Designer
K. Rohn under the supervision of Dr. A. Brill
München in 1877

Company
Martin Schilling in Halle a.S.

Original price
Mark 7,-

Dimension
10-10-18 cm

Material
Plaster

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