Constructing a Sphere out of Paper

Date: 02/08/2003 at 15:37:35
From: Camille
Subject: Flattening a sphere (constructing a sphere out of paper)

Hi, 

I'm hoping you might be able to help me. I'm working on a school 
project and can't seem to find the answer anywhere. The assignment is 
to construct a 3D 9"-diameter sphere out of paper. 

Isn't there some standard format or template for figuring this out? 
Thank you.

Date: 02/08/2003 at 18:07:53
From: Doctor Jodi
Subject: Re: Flattening a sphere (constructing a sphere out of paper)

Hi Camille,

What a challenging project!

You can find information about how spheres are made from cubical 
chunks:

   How to make a sphere page
   http://www.maxpages.com/thundereggs/How_to_make_Spheres 

And a friend of mine has some pictures and an explanation of why you 
can't make a sphere out of paper. Basically, a sphere is REALLY curved 
(this file is in PDF format):

   http://193.75.136.15/~dhuylebrouck/Matomium/Goodman_Strauss2.pdf 

You can also see a discussion of a math teacher's approach at 

   Making Hemispheres out of Paper
   http://mathforum.org/library/drmath/view/55168.html 

Basically, this math teacher decided to make a polyhedron with a 
number of sides. A polyhedron is a 3D shape made of polygons. The cube 
and pyramid are the most common polyhedra, but there are lots of 
others. You can see the next two links for pictures and info about 
constructing polyhedra.

   Virtual Polyhedra - George W. Hart
   http://www.georgehart.com/virtual-polyhedra/vp.html 

   Stella: Polyhedron Navigator -  Robert Webb
   http://www.software3d.com/Stella.html 
 
Hope this helps! Please let us know how the constructing goes. Write 
back if you think we could be of more help.

- Doctor Jodi, The Math Forum
  http://mathforum.org/dr.math/