Looking at country shapes is a hard way to judge a map, because few of us know the true shapes well. Mapmakers have a better test, invented by the French mathematician Nicolas Auguste Tissot in papers from 1859 to 1871. It uses circles. You already know the projections from Compromise Maps.
Key idea
Draw same-size circles all over the globe, then project them. Where the circles get bigger, the map enlarges areas. Where they turn into ovals, it bends shapes. Circles that stay round and the same size mean no distortion there.
Why it works
A tiny circle on the globe is the simplest test shape: it has the same width in every direction. If a projection stretches more in one direction than another, the circle becomes an oval; if it stretches equally in all directions, the circle stays round but changes size. So the circles show both kinds of distortion at once.
| What the circles do | What the map keeps | Example |
|---|---|---|
| Stay round, but grow toward the poles | Shapes (angles); areas grow | Mercator |
| Become ovals, but keep the same area | Areas; shapes bend | Gall-Peters, Mollweide, Equal Earth |
| Change a little in size and shape | Neither exactly; small errors | Robinson, Winkel tripel |
Worked example: Reading a Tissot map
On a map, the circles near 60° N are perfectly round but about twice as wide as the circles on the equator. What kind of map is it?
- Round circles mean shapes are kept.
- Circles twice as wide cover about four times the area, so areas are enlarged there.
- Keeping shapes while enlarging areas toward the poles is what Mercator does.
Answer: A Mercator map (it keeps shapes; areas at 60° look 4 times too big).
Worked example: Ovals
On another map, circles near the poles are squashed into wide, flat ovals, but each oval covers the same area as the circles at the equator. What does the map keep?
- Same area everywhere: areas are true.
- Ovals: shapes are bent.
Answer: It is an equal-area map.
Common mistake
Judging a map by whether the countries "look right." Your idea of how countries look may come from Mercator maps. The circles are a fair test: compare their sizes to judge area, and their roundness to judge shape.