At
The Economist, via
Ritholtz:
A sphere cannot be represented on a flat plane without distortion,
which means all map projections distort in one way or another. Some
projections show areas accurately but distort distances or scales, for
example; others preserve the shapes of countries but misrepresent their
areas. You can read all the gory details on Wikipedia.
Gerardus
Mercator's projection, published in 1569, was immediately useful
because it depicts a line of constant bearing as a straight line, which
is handy for marine navigation. The drawback is that it distorts the
shapes and areas of large land masses, and the distortion gets
progressively worse as you get closer to the poles. (Africa looks about
the same size as Greenland under the Mercator projection, for example,
even though it is in fact 14 times bigger.) This was not a big problem
for 16th-century sailors, of course, and the Mercator projection remains
popular to this day.
In Mr Krause's map (above) he seems to have
used the shapes of the countries from a Mercator projection, but has
scaled up the outline of Africa, without changing its shape, to show the
appropriate area. An alternative and arguably more rigorous approach
would be to repeat the exercise using an "equal area" projection that
shows the countries' areas correctly while minimising shape distortion.
The curvature of the earth stuff in surveying throws me for a loop. I'll leave that stuff up for other folks.
No comments:
Post a Comment