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Serie VIII, Nr 3

Surface of order 12; the enveloping surface of a system of rays.


  

Mathematical description
Surface of order 12. This model is from geometrical optics. Rays of light from a source perpendicular to a cylinder-axis are reflected in the cylinder:

                x = r cos(φ)
                y = r sin(φ)
                z = z,
The model shows the surface, which is enveloped by all these reflected rays. This surface is given by the following equation:
[(4z2-r2)(x2+y2)-r2z(2x+z)]3 -27r44z2y2(x2+y2-z2)2=0,
when z is the distance between the cylinder and the lightsource.

Title model and translation
Fläche zwölfter Ordnung, Brennfläche.
Surface of order 12; the enveloping surface of a system of rays.

Text on Sticker and translation
Fläche 12. Ordnung.
Surface of order twelve.

Designer
S. Finsterwalder under the supervision of Dr. Brill
München in 1882

Company
L. Brill in Darmstadt

Original price
Mark 17

Dimension
13-20-12 cm

Material
Plaster

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