Drexel dragonThe Math ForumDonate to the Math Forum

Ask Dr. Math - Questions and Answers from our Archives
Associated Topics || Dr. Math Home || Search Dr. Math

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 

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

Best regards,
- Doctor Floor, The Math Forum
Associated Topics:
High School Conic Sections/Circles
High School Definitions
High School Geometry
High School Triangles and Other Polygons

Search the Dr. Math Library:

Find items containing (put spaces between keywords):
Click only once for faster results:

[ Choose "whole words" when searching for a word like age.]

all keywords, in any order at least one, that exact phrase
parts of words whole words

Submit your own question to Dr. Math

[Privacy Policy] [Terms of Use]

Math Forum Home || Math Library || Quick Reference || Math Forum Search

Ask Dr. MathTM
© 1994-2015 The Math Forum