"A globe is, of course, the only possible medium for showing all geograpical relationships in true perspective...But globes have a serious drawback:they are limited in scale. A globe which would show a continent on the same scale as most standard maps would have to be two, three, perhaps four meters in diameter."
John Noble Wilford from The Mapmakers

Table of Contents
Maps Main Page
What are Maps?
Map History
Math Topics
Math Problems
Web Resources
Careers
Teachers' Notes
References
Other Math Lessons

Mathematics of Cartography

Mathematics Topics-Projections


Round Earth, Flat Map
from National Geographic

Make a Map Projection
From a Soda Bottle

Map projection
A function or transformation which relates coordinates of points on a curved surface to coordinates of points on a plane.
Exercises in Oceanography
Great info on projections
A Problem
If you cut a cylinder apart lengthwise, you can lay it flat. (Think about a can label). Can you cut apart a sphere and lay it out flat?

Distortion is inevitable when we try to project the points of a 3-dimensional earth onto a 2-dimensional piece of paper (or computer screen). Angles, areas, directions, shapes and distances can become distorted when transformed from a curved surface to a plane. Many different projections have been designed where the distortion in one property is minimized, while other properties become more distorted.


More Great info
For Example
The Mercator Projection Angles are preserved, but distances away from the equator become progressively distorted. (South America is actually nine times as big as Greenland.
Another Example
See how much this changes your perspective!
The Peters Projection was created in 1974 to address some of the distortions of existing maps. Peters Map preserves sizes and proportions. One square inch anywhere on this map represents an equal number of square miles.

Map Projections
More Info
The Mercator projection is called Conformal A projection is conformal if the angles in the original features are preserved.
  • Over small areas the shapes of objects will be preserved.
  • A line drawn with constant orientation (e.g. with respect to north) will be straight on a conformal projection (a rhumb line).
  • Parallels and meridians cross each other at right angles (note: not all projections with this appearance are conformal).
  • Generally, areas near margins have a larger scale than areas near the center (i.e. Greenland in Mercator projection).
A Gallery of Projections
At The Great Gallery Globe you will find examples of several different projections. Remember, the cartographer chooses the projection which most closely fits the purposes of her map.
Table of Contents
Maps Main Page
What are Maps?
Map History
Math Topics
Math Problems
Web Resources
Careers
Teachers' Notes
References
Other Math Lessons

Email any comments to lanius@math.rice.edu
Copyright 1996-2004 Cynthia Lanius

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