Göttingen Collection of Mathematical Models and Instruments

Cone of third order

Model 80

A IV 5


Cone of third order and genus 0. Fiber model.


The thread models 80-86 are cones over planar curves, and serve to study them in projective geometry; in that geometry, "points" are lines through the cone point.

Newton (Enumeratio linearum tertii ordinis, 1706) initiated the study of planar curves of degree 3; the work was continued by Plücker, Cayley, and Möbius.

The base of this cone is a singly cusped cubic of genus 0 (namely, rationally parametrizable), called semi-cubic parabola; and the space curve made of brass is the intersection of the cone with a sphere. The equation is $x^2y-z^3=0.$

This model was designed by Prof. H. Wiener in the 1890s.

Showcase of this model is Case number 8


Schilling, Martin(Hrg.): Catalog mathematischer Modelle, Leipzig(Verlag von Martin Schilling) 1911, 7.Auflage, No.78. p. 122.

Hermann Wiener(1901). Die Einteilung der ebenen Kurven und Kegel dritter Ordnung in 13 Gattungen, Verlag von Martin Schilling, Halle a. S.. Online version