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Serie XVII, Nr 1

Model of a minimal surface which contains a group of real parabolas.


Mathematical description
This model is a minimal surface. A minimal surface is a surface with zero mean curvature. The mean curvature H of a surface is defined as:
H = k1+k2
2
where k1 and k2 are the principal curvatures of the surface (i.e., the maximum and minimum of the normal curvature K at a given point of a surface).
A minimal surface is given by the Enneper-Weierstrass parametrization. For this model the parametrization is given as follows:

                       x = 6sin(2φ) - 12φ + 12vsin(φ) + 3v2sin(2φ)
                       y = -6cos(2φ) - 12vcos(φ) - 3v2cos(2φ)
                       z = 24φ + 12vsin(φ)
The model is representing a minimal surface containing a group of real parabolas.

Title model and translation
Modell einer Minimalfläche welche eine Schar reeller Parabeln enthält.
Model of a minimal surface which contains a group of real parabolas.

Text on Sticker and translation
Minimalfl. mit reeller Parabelnschaar.
Minimal surface with real Parabola group.

Designer
Hj. Tallqvist under the supervision of Dr. E. R. Neovius
Helsingfors in 1886

Company
Martin Schilling in Halle a.S.

Original price
Mark 45

Dimension
21-24 cm

Material
Plaster

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