Previous Serie XVII Next

Serie XVII, Nr 4

Model of the Catalan's minimal surface.


  

Mathematical description
This model is an example of an Enneper surface. An Enneper surface is a minimal surface that intersects itself. 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).
The Catalan's surface is given by the following parametrization:

                    x = 12sin(2φ) - 24φ + 6v2cos(2φ)
                    y = -12cos(2φ) - 6v2cos(2φ)
                    z = 24vsin(φ).

Title model and translation
Modell der Catalan'schen Minimalfläche.
Model of the Catalan's minimal surface.

Text on Sticker and translation
Missing sticker.

Designer
J. Laine under the supervision of Prof. Dr. E. R. Neovius
Helsingfors in 1886

Company
Martin Schilling in Halle a.S.

Original price
Mark 45

Dimension
22-22-14 cm

Material
Plaster

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