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Serie XVII, Nr 2b

The seven types of plane curves of order three principal.


Mathematical description
This models represents a sphere with three of the seven principal types of plane curves of order three on it. The equations from the three plane curves are from the inside til the outside:

                    y2 = 4/9 [(x+3)2 - 20 x3 / (x-4)]
                    y2 = 4/9 [(x+3)2 - 25 x3 / (x+6)]
                    y2 = 4/9 [(x+3)2 - 20 (4x)3 / (x+3)]
This plane curves are projected on the sphere with projective geometry.

Title model and translation
Die sieben Haupttypen der ebenen Curven 3. Ordnung.
The seven types of plane curves of order three principal.

Text on Sticker and translation
Kugelprojection d. ebenen Curven 3.Ord. II 3 typen
II. Three types spherical projection even curves of order three.

Designer
Dollinger under the supervision of Dr. Brill
Tübingen in 1886

Company
Martin Schilling in Halle a.S.

Original price
Mark 12 (two pieces)

Dimension
10 cm

Material
Plaster

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