Mapmaking - The Science of Navigation - page 95

length that equals the globe circumference and a height that equals the
globe diameter; any mathematician will tell you that your piece of paper
therefore has the same surface area as the globe. Yet try to glue the paper to
the globe —go on, try it! You may do so without di≈culty all the way
around the equator, for example, but then you will find that the paper will
not reach the poles.
In short, to make a 2-D representation of a 3-D globe, we need to stretch
the paper at some points and compress it at other points. 5 This stretching
and compressing leads to distortion and is the basic reason why all maps
are distorted.
So why bother with maps? Let's just make 3-D globes. They have the
advantage that they truly represent our earth in miniature. All the direc-
tions from one place to another are true; all the sizes and shapes of the
continents represented on our globe are true miniature representations of
the earth's continents. Unfortunately, the disadvantages of globes outweigh
their advantages. Globes are expensive to make, to reproduce, and to keep
up to date. They are bulky and so are inconvenient to store and transport.
Finally, because they are necessarily small-scale, they cannot provide us
with much detail: when was the last time you took a globe on vacation to
help you navigate?
Cartographers from centuries ago were well aware of the shortcomings
of globes and also of the distortions that resulted when trying to reduce
globes to a 2-D surface. Let us examine the various options that exist and
look at their advantages and disadvantages so that we can understand why
real maps of the world evolved in the way that they did.
Projections
Consider two points A and B on the surface of the earth. These points
will lie a certain measurable distance from one another, and to get directly
from A to B we travel in a certain well-defined and measurable direction.
Consider this distance and direction to have been already determined.
Translating the coordinates of latitude and longitude from a 3-D globe onto
a 2-D map ( projecting the globe onto a plane, in the language of geogra-
phers) introduces distortions that may result in A and B being separated by
the wrong distance, or may result in the direction between them being
5. If the paper has the same area as the globe, and if it needs to be stretched to reach the
poles, then it has to be compressed somewhere else.