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Serie I, Nr 2a

The enveloping surface of a system of rays of a paraboloid. The two components separated.


  

Mathematical description
This model is from geometrical optics. Parallel rays of light are coming, almost parallel to the x-axis and are reflected in the paraboloid:

                 y2    z2
                --- + ---  = 2x
                 12    10       
The models show the surfaces S wich are enveloped by all these reflected rays. These kind of surfaces were described by P. L. von Seidel (1821-1896). In the present case:
S = { (x,y,z) | ∃v 24y2=(v-1)3(3v+1-2x) }
-24z2=(v+1)3(3v-1-2x)
The surface has two components that are represented in the models separately.

Title model and translation
Die Brennfläche eines Strahlensystems. Die beiden Mäntel der Fläche getrennt.
The enveloping surface of a system of rays of a paraboloid. The two components separated.

Text on Sticker and translation
Centrafläche des Paraboloids.
The enveloping surface of a system of rays of a paraboloid.

Designer
L. Schleiermacher under the supervision of Prof. Dr. A. Brill
München in 1877

Company
Martin Schilling in Halle a.S.

Original price
Mark 6,-

Dimension
10-10 cm and 7-7 cm

Material
Plaster

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