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/