M. Schilling catalog

Three-axial ellipsoids

Lines of curvature–Classification of surfaces of 2nd order–Ellipsoids and spheres

#quadric#ellipsoid#three-axial#lines of curvature#umbilical point#Diesel#Brill

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Three-axial ellipsoids

Date of design: 1878

Designer: R. Diesel under supervision of Prof. Dr. L. Brill

Title in the catalog: (de) 1). Ellipsoid, grosse Halbaxe 5 cm. Axenverhältnis $\sqrt{3} \colon \sqrt{2} \colon \sqrt{1}$; 2). Dasselbe mit Krümmungslinien; 3). Ellipsoid, grosse Halbaxe 9 cm. Axenverhältnis $\sqrt{3} \colon \sqrt{2} \colon \sqrt{1}$; 4). Dasselbe mit Krümmungslinien

Price in the catalog: resp., 1.60, 3.20, 2.25, 8 marks (1911)

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Description

Models of three-axial ellipsoids of various sizes given in the standard Cartesian coordianates by the equation

$\frac{x^2}{3} + \frac{y^2}{2} + \frac{z^2}{1} = a^2$,

where $a$ is a real parameter.

Each size has the second version with the (orthogonal) net of curvature lines. Models also show locations of umbilical points - singular points of such nets.



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