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### Degenerate/Nondegenerate Figure

```
Date: 10/27/2001 at 16:26:11
From: Jan Roy
Subject: Incidence geometry

We need to know what a nondegenerate circle is. (We're trying to
decide whether or not this is a model of incidence geometry, but we
don't know what the definition is.)
```

```
Date: 10/29/2001 at 05:48:16
From: Doctor Floor
Subject: Re: Incidence geometry

Dear Jan,

A circle is called degenerate if:

- the length of the radius is zero, so the circle is a single point,

- the length of the radius is infinite, so the circle is a straight
line.

In other cases the circle is nondegenerate.

Other geometrical figures can also be degenerate. The degenerate
figures always are very special cases, in which the figure is not what
one would expect. For instance, a triangle is degenerate if the three
vertices lie on a line (or even coincide).

Degenerate Conics
http://mathforum.org/dr.math/problems/kiczek3.4.98.html

Best regards,
- Doctor Floor, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Conic Sections/Circles
High School Definitions
High School Geometry
High School Triangles and Other Polygons

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