Just as if you attempt to construct two parallel lines by intersecting a plane with a cone. Or as if you attempt to construct a circle with the focus-directrix definition. The whole area of "limiting cases" is an embarrassment: We keep what's convenient, and tell students that the rest is nonsense. Nonsense. Rich -----Original Message----- From: math-fun-bounces+rschroe=sandia.gov@mailman.xmission.com on behalf of Fred lunnon Sent: Sat 2/17/2007 7:04 AM To: math-fun Subject: Re: [math-fun] Re: sections of quadratic surfaces On 2/17/07, Emma Cohen <emma@don-eve.dyndns.org> wrote:
But this reminds me of something that used to bother me in high school when I learned about conic sections: Was anyone else annoyed that a line segment (which can be defined as the set of all points X such that |AX| + |BX| = |AB| and hence seems to be a sort of ellipse under one common definition) is not in fact a conic section?
Isn't this definition of a line segment just an ellipse whose minor axis is zero?
However, if you attempt to construct a finite line segment as the intersection of a plane with a cone --- the origin of the term "conic section" --- you will find it impossible, WFL _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun