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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.

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/
```
Associated Topics:
High School Conic Sections/Circles
High School Definitions
High School Higher-Dimensional Geometry

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