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:
x^{2} y^{2} z^{2} --- + --- — --- = 1 5^{2} 2^{2} 1^{2}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 | 20y^{2}=(v-5/2)^{3}(3v+5/2+x^{2}/25) | } |
-5z^{2}=(v+5/2)^{3}(3v-5/2+x^{2}/25) |
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