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Serie XIII, Nr 5

Ruled surface with self intersection forming a line and with four Pinchpoints on the line.


  

Mathematical description
A ruled surface is a surface that can be swept out by a moving line 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. In this case, the surface has order four and it is embedded in P3.
The surface consist of two components and is given by the following equation:
a(x4+y4) + 2bx2y2 + c(xw-yz)2 = 0,
where b/a<-1. It has one real double line, where the two sheets intersect themself. The double line is marked with a blue string and on it are four pinch points. A pinch point is a singular point such that every neighborhood of the point intersects itself. Pinch points are also called Whitney singularities or branch points.

Title model and translation
Regelfläche mit einer Selbstberührungsgeraden und vier Pinchpoints auf derselben.
Ruled surface with self intersection forming a line and with four Pinchpoints on the line.

Text on Sticker and translation
Regelfl. mit selbstberührungsgerad.
Ruled surface with curve with self intersection.

Designer
Dr. Karl Rohn
Dresden in 1886

Company
Martin Schilling in Halle a.S.

Original price
Mark 42

Dimension
18-18-18 cm

Material
String

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