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# 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:
*y*^{2}*z*=*x*^{2}(*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