Projection Lab中文

How many Frances fit in South America?

28 Frances fit in South America.

Really
28
As Mercator draws it
16

Mercator makes it look like only 16, fewer than the 28 that really fit. This time the container is the one nearer the equator, and so the one inflated less.

Drawn to scale

The two places at one scale, side by side. South America is painted the same size in both panels, so the only thing that changes is France - and how much it changes on the Mercator side is exactly how far that map moves the count.

  1. Equal Earth28 Frances
  2. Mercator16 Frances

The two are drawn beside each other, not packed one inside the other. What the picture gets exactly right is the ratio of the areas; whether irregular shapes would actually tile without gaps is a different question, and this figure does not answer it.

Why the two differ

Mercator draws France 1.97 times its true area and South America 1.17 times. The count is the ratio of the two, so what moves it is not the inflation itself but the ratio between the two inflations. Whichever sits closer to a pole is blown up more.

Ruler
France 643,775 km²
Container
South America 17,815,855 km²

What each projection says

Every row is the ratio of the areas that projection paints for itself, not a figure converted from another projection's baseline. The two equal-area members return the true count, which is their definition rather than a coincidence.

ProjectionCount as drawn
Equirectangular21
Mercator16
Natural Earth23
Equal Earth28 true
Gall-Peters28 true

On an equal-area projection

Under Equal Earth or Gall-Peters the two figures are identical - for every pair on this site. An equal-area projection draws in proportion to true area, so the count you can see is the count there is. That is a definition, not a coincidence.

Open on Equal Earth

Next door

France somewhere else

Something else in South America