Conical Vertex?

Date: 03/27/2003 at 14:18:42
From: Bluey
Subject: Conical vertex?

Greetings, Dr. Math!

I'm a 3rd grade teacher, but have taught secondary math in the past. 
Usually, in class we define a "vertex" as a point where two sides/
edges meet to form an angle.

When we arrived in solid/space goemetry, we were perplexed as to 
what the point at the tip of a cone is called. If we use the former 
definition, "vertex" doesn't work. Help!

Date: 03/27/2003 at 14:57:38
From: Doctor Peterson
Subject: Re: Conical vertex?

Hi, Bluey.

I prefer "apex", which distinguishes it, in the case of a pyramid, 
from the vertices of the base. But in fact the original meaning of 
"vertex" is "highest point," making these words synonymous!

Here is the definition of "vertex" from Merriam-Webster:

  1 a : the point opposite to and farthest from the base in a figure
  b : a point (as of an angle, polygon, polyhedron, graph, or
  network) that terminates a line or curve or comprises the
  intersection of two or more lines or curves c : a point where an
  axis of an ellipse, parabola, or hyperbola intersects the curve
  itself
  2 : the top of the head
  3 : a principal or highest point : SUMMIT <the vertex of the hill>

Even within math, as this shows, the word "vertex" has several 
different, though related, definitions. The definition requiring that 
edges meet at a vertex is used for polyhedra (and also in graph 
theory), but does not apply in the case of cones. Either "vertex" 
or "apex" is appropriate.

This page will be of interest to you, as well:

   Number of Cylinder Edges
   http://mathforum.org/library/drmath/view/54701.html 

If you have any further questions, feel free to write back.

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/