# Serie XXV, Nr 3

## Generalized cone of order three of genus zero, with a return side.

Explanation
This is a model representing a generalized cone. The cones are special cases of ruled surfaces. 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) + v δ(u),
```
where b is called the director line (or directrix) and δ is the director curve.
A generalized cone is a ruled surface that can be parametrized by
```                 x(u,v) = p + v δ(u),
```
where p is a fixed point which can be regarded as the vertex of the cone. This model is given by an homogeneus equation of degree three:
y2z=x2(x-z).
The model represents a cone of genus 0. This means that the intersection of this model with a plane gives a curve with a singularity. In this case, the intersection is a isolated point and a smooth curve.

Title model
Kegel dritter Ordnung vom Geschlechte Null. Kegel mit Rückkehrkante.
Generalized cone of order three of genus zero, with a return side.

Information sticker
Missing sticker.

Designer
Prof. Dr. H. Wiener
Darmstadt in 1899

Company
Martin Schilling in Leipzig

Original price
Mark 18

Dimension
17 cm

Material
String

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