Map Projections

Date: 04/26/99 at 21:24:27
From: Arm Sarkissian
Subject: Maps

I have a math project due. The question is:

Demonstrate the mathematics of creating a flat map of a curved object.

I am totally stumped. Can anyone help me?

Thanks.

Date: 04/27/99 at 11:43:56
From: Doctor Rick
Subject: Re: maps

Hello, Arm, welcome to Ask Dr. Math!

Your topic is called "map projections." It's a fascinating topic; 
there is a lot that you could say about this, with some nice pictures 
too. I hope you enjoy learning about it.

The basic problem is this: You can't peel an orange and flatten the 
peel without tearing it. To put it the other way, you can't wrap 
aluminum foil around a tennis ball without crinkling the foil. There 
is no one perfect way to make a flat map of the round earth. People 
have come up with many ways to do the job; each is good for some 
purposes and really bad for others.

Here is one Web site that contains details of lots of map projections.

  Map Projection Overview
  Peter H. Dana, Dept. of Geography, University of Texas at Austin
  http://www.utexas.edu/depts/grg/gcraft/notes/mapproj/mapproj.html   

You might find this site a little easier to follow:

  World of the Atlas: Map Projections (Jan-Willem van Aalst)
  http://is.twi.tudelft.nl/~jwva/atlas/mprojec.htm   

Neither of these goes into actual mathematical equations for a map
projection, as far as I could see, but you might be able to work out a
simple example like a cylindrical projection. You'll probably want to 
go over how latitude and longitude work before you try this.

Also see Cynthia Lanius' site:

  The Mathematics of Cartography
  http://math.rice.edu/~lanius/pres/map/   

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