Types of Cones Date: 01/19/99 at 15:57:04 From: Jamie Rowan
Subject: Edges of cones Does a cone have an edge? Date: 01/20/99
at 08:55:54 From: Doctor Rob Subject: Re: Edges of cones There
are several meanings to the word "cone." In some, it does not
have an edge; in others, it does. I will try to describe the
various meanings precisely and perhaps then you will see what I
mean. Set up a Cartesian rectangular xyz-coordinate system as
follows. Take the origin to be the vertex of the cone, and the
z-axis to be the axis of the cone. Then a right circular cone
can be defined by an equation of the form a^2*z^2 = x^2 + y^2
for some nonzero constant a. The words "right circular" mean
that a cross-section perpendicular (at a right angle) to the
axis is a circle. Often these words are omitted, since it is
quite uncommon to see an oblique circular cone or a right
elliptical cone, or other types. An "infinite right circular
cone of two sheets" consists of all points whose coordinates
satisfy this equation. In this form,