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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). 

See also from the Dr. Math archive:

   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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