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Serie XIII, Nr 4

Ruled surface with two conjugated imaginary double lines.


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 model represents a ruled surface of degree four embedded in P3.
The two lines are complex conjugated so the real picture of this surface does not show the singularities. The equation of the surface, in four homogeneous variables, reads:
(x2+y2)2 + (z2+w2)2 + 2b(xz-yw)2+2c(xw+yz)2 = 0
with either b<-1 or c<-1. On the surface are two double lines, they are complex conjugated so the real picture of this surface does not show the singularities.

Title model and translation
Regelfläche mit zwei conjugiert imaginärien Doppelgeraden.
Ruled surface with two conjugated imaginary double lines.

Text on Sticker and translation
Regelfl. mit 2 conjug. Imag. Doppelger.
Ruled surface with two conjugated imaginary double lines.

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