# Cone of third order

### Model 80

### Description

Cone of third order and genus 0. Fiber model.

### Additions

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

### References

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