Does a Sphere have Sides?Date: 04/20/2001 at 09:13:12 From: Sarah and Stephany Subject: Sides of a sphere Our question is, how many sides does a sphere have? We feel this is an opinion question. Is there an answer that is right all over the world? From Sarah and Stephany Date: 04/20/2001 at 10:18:28 From: Doctor Peterson Subject: Re: Sides of a sphere Hi, Sarah and Stephany. I'd say it's a definition question: what do you mean by "side"? The problem is that this word does not have a single definition that is used in all circumstances; even among mathematicians, it is usually replaced by more carefully defined terms such as "face," "edge," or "boundary," rather than being given a precise definition. Sometimes we think of sides as having to be flat - what mathematicians call "faces" of a polyhedron. In that sense, a sphere has no sides (though some people will try to convince you that it has infinitely many sides). I think the most applicable definition is the one used in topology. We talk about surfaces with two sides (like a piece of paper) and surfaces with only one side (like the Moebius strip you may have heard of). In this sense, and remembering that mathematicians define a sphere as the surface of a sphere, not a solid ball, I would say that a sphere has two sides: the outside and the inside. That may sound like a joke, but it's really the best mathematical answer I can give. Here is an answer to a related question from our archives: Is a Circle a Polygon? http://mathforum.org/dr.math/problems/tyler03.07.99.html - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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