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Serie I, Nr 3a

The enveloping surface of a system of rays of a one sheeted hyperboloid. The two components separated


  

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, represented in the models separately.

Title model and translation
Die Centrafläche des einschaligen Hyperboloids. Die beiden Mäntel der Fläche getrennt.
The enveloping surface of a system of rays of a one sheeted hyperboloid. The two components separated.

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

Designer
W. Dyck under the supervision of Dr. A. Brill
München in 1877

Company
Martin Schilling in Halle a.S.

Original price
Mark 9,50 and Mark 10,50

Dimension
17-17-16 cm

Material
Plaster

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