Names of Parts of a Cone

Date: 8/2/96 at 19:31:33
From: Bonnie Seiler
Subject: Names of Parts of a Cone

Hi Dr. Math! 

I'm interested in the components of the net of a cone.  Are the 
components of a net called faces in all cases, or only for polyhedra?

Could you please tell me what the wedge-like "face" is called?  It's
actually a sector of a circle, I guess.  

Also, can you refer to "faces" of a cone and cylinder, or are they 
not faces, since they are curved instead of flat?

Can you recommend any sources for information on nets of basic 3D 
figures (say grade school through grade 6)?

Date: 10/24/96 at 10:33:16
From: Doctor Tim
Subject: Re: Names of Parts of a Cone

As to the name for that curved surface (is it a face?) I have to admit 
I don't know and the people I asked didn't know either, and neither 
did the book we consulted. The dictionary at my side, however, (a 
Webster) defines face partly as a "principal or bounding surface" so 
in that sense it may well apply. But I have to admit it "feels" wrong, 
and, as a writer, I might avoid it since it might make the reader 
stumble and be confused (unless you set it up really well and use it 
consistently).

As for me, I always call it "the curved surface of a cone," which also 
works for cylinders. And you can always use graphics!

You're right, by the way, that the curved surface is a sector of a 
circle (unlike a sphere, it lies flat). Interestingly enough, when 
that sector is a semicircle, the cross-section of the resulting cone 
that goes through its vertex is an equilateral triangle. More of the 
circle, it's flatter; less, it's more pointy.

-Doctor Tim,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/   

Date: 10/24/96 at 10:47:44
From: Doctor Ken
Subject: Re: Names of Parts of a Cone 

Hi Bonnie -

There's a computer program for constructing nets of 3D figures, called 
HyperGami.  For more information, see   

  http://mathforum.org/~sarah/HTMLthreads/articletocs/hypergami.paper.sculpture.html   

There's also a Math Forum web page about polyhedra and how to build 
them.  You can find it at:

http://mathforum.org/sum95/math_and/poly/polyhedra.html   

A good place to start looking for things like this is the Math Forum 
searcher, at 

  http://mathforum.org/grepform.html   

Happy netting!

-Doctor Ken,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/