Degenerate/Nondegenerate FigureDate: 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/ |
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