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Serie VII, Nr 23

Surface of order three. Cayley's ruled surface with a cuspidal point (at finite distance).


Mathematical description
When a cubic surface has more than 4 double points must be singular along and entire curve. In this case, the surface is a ruled surface, i.e., it is swept out by a line moving in space. It has a parametrization of the form:

                x(u,v) = b(u) + vδ(u),
where b is called the director line (or directrix) and δ is the director curve.
The model represents the Cayley's ruled surface. It is a cubic ruled surface in which the director line meets the director curve. The Cayley's surface is the unique cubic surface having four ordinary double points, the maximum possible for a cubic surface.

Title model and translation
Fläche dritter Ordnung. Cayley'sche Regelfläche mit (unendlich fernen im Endlichen gelegenen) Cuspidalpunkte.
Surface of order three. Cayley's ruled surface with a cuspidal point (at finite distance)

Text on Sticker and translation
Regelfläche 3. Ordnung.
Ruled surface of order three.

Designer
Dr. Carl Rodenberg
Darmstadt in 1881

Company
L. Brill in Darmstadt

Original price
Mark 16,50

Dimension
13-15 cm

Material
Plaster

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