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/
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