Defining a Sphere

Date: Thu, 01 Dec 1994 22:27:38 -0400 (EDT)
From: Kendall
Subject: Sphere

Dear Dr. Math,  My math teacher asked me to send you this math question.
There seems to be different information about spheres in our old math book
and our new one.  

        Addison-Wesley _Mathematics_ 1987 shows:
        A sphere has Zero flat faces, Zero vertices, Zero straight edges,
        Zero curved edges and ONE curved face.
 
        Harcourt Brace Jovanovich _Mathematics Plus_ 1992 shows:
        The same information EXCEPT it says ZERO curved faces.

Is one right and the other wrong or has someone made a change? My teacher
needs to know which way it should be taught. 

Thank you in advance for your help.

- Kendall

Date: 7 Dec 1994 01:35:35 GMT
From: Dr. Math
Subject: Re: Sphere

Hello there Kendall!

Many mathematicians have intense debates over how to define objects like
this.  The problem is that nobody is right and nobody is wrong, since you
can define anything you want to define, and then you see what those
definitions give you.

I must admit, I tend to agree with the first definition of the sphere,
because when I look at a sphere, I see a curved face.  When I try to
picture the sphere they described with ZERO curved faces, I have a tough
time with it.  It doesn't make sense to me.

Of course, I have an entirely different definition of sphere that I like. 
I define it as the set of points that are equidistant from a given point. 
That point is the center of the sphere.

So it's kind of a matter of personal preference, since every good
definition of something is equivalent to every other good definition of it.

I hope this helps the debate.