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:
y^{2} z^{2} --- + --- = 2x 12 10The 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 | 24y^{2}=(v-1)^{3}(3v+1-2x) | } |
-24z^{2}=(v+1)^{3}(3v-1-2x) |
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