M. Schilling catalog

Sphere as a rotationally symmetric surface of constant positive Gaussian curvature

Ellipsoids and spheres–Surfaces of revolution of constant Gaussian curvature

#sphere#quadric#constant curvature#constant Gaussian curvature#surface of revolution#Brill

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Sphere as a rotationally symmetric surface of constant positive Gaussian curvature

Date of design: 1880

Designer: E. Bour (calculations), P. Vogel under supervision of Prof. Dr. L. Brill in TU München

Title in the catalog: (de) Rotationsflächen von konstantem positiven Krümmungsmaß mit geodätischen Linien (drei Typen mit gleichem Krümmungsmaß). a) Die Kugel.

Size: 9 cm

Price in the catalog: 1.20 marks (1911)

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Description

Sphere is the only smooth and complete surface of constant positive Gaussian curvature.

The model falls in the family of rotationally symmetric surfaces of constant Gaussian curvature (see the spindle-shaped surface and the cheese-shaped surface).

Presence of a brass plate represent homogenity of surfaces of constant curvature - one can slide the plate along the surface without losing a complete contact with the surface.

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