Do Cones and Cylinders Have Faces or Surfaces?
Date: 03/16/2004 at 08:22:25 From: Rhonda Subject: Does a cone have faces? Does a cone have faces or are they called curved surfaces and a base? The same question can be asked for a cylinder. Are the ends faces or bases and is the curved surface also considered a face? I have seen different books with different answers. Some also say that a cone does not have a vertex.
Date: 03/16/2004 at 09:08:30 From: Doctor Peterson Subject: Re: Does a cone have faces or are they really called curved surf Hi, Rhonda. Here are some discussions of this question from our archives: Cone, Cylinder Edges? http://mathforum.org/library/drmath/sets/select/dm_cone_edge.html Too many texts ask this question, which really shouldn't be asked. The problem is that there is no standard definition for these terms outside of polyhedra. If they want to talk about faces on a cylinder, they need to define the term in a way that applies to it: either insist that a face must be flat (and, for some, a polygon), and provide a different term for curved or round surfaces; or extend the definition to cover any distinct surface, flat or curved. But when they do that, they will be disagreeing with someone's usage! It's probably better to use a different term, as some texts do, and just call them "surfaces", without talking about "faces" in this context at all. I offer some relevant thoughts on the role of definition at the bottom of this long page: Definitions as a Tool of Mathematics http://mathforum.org/library/drmath/view/62384.html Definitions are more flexible than non-mathematicians realize; we take a basic idea like "vertex" and adjust it to fit the object we are studying (polygons, polyhedra, curves, networks, ...); therefore we have to state our definitions at the start of a paper in order to clarify how we are using terms. Elementary texts, on the other hand, need to teach standard definitions that are used everywhere, since they are only introducing concepts without elaborating them yet, and can't just offer a definition for the sake of their discussion. Therefore, they need to discuss only those definitions that ARE common, and avoid areas like this where no consensus exists--or is needed. Authors and teachers need to ask, what is the value in the concept I want to teach? If it has no value other than introducing the meaning of a word, and that word is not clearly defined, then drop it. If it is useful (like being able to talk about the parts of a cylinder), then choose terms that allow you to do so. Saying that a cylinder has no faces doesn't allow you to talk about the parts of a cylinder, does it? So "face" shouldn't be defined that way for this purpose. Either redefine it, or talk about the "lateral surface" and the "bases" or "circular faces" or whatever you want to call them. 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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