In Globe or Flat Map? you saw that a globe is the truest picture of Earth, but a flat map is easier to carry and shows the whole world at once. Now let us see what the flat map gives up.
Key idea
You cannot flatten a ball without stretching or tearing it. So every flat world map distorts something: sizes (areas), shapes, distances or directions. A map projection is a mapmaker's method for moving the grid of the globe onto flat paper, and each one chooses what to keep true.
Why it works
Try it with an orange. Peel it and press the peel flat: it splits, or you have to squash and stretch it. Earth's surface is curved in every direction at once, so no flat sheet can match it everywhere. The mathematician Leonhard Euler proved in 1775 that no flat map can keep every distance true. A flat map can keep areas true, or keep shapes true in small areas, but not both.
| What a map can keep | What it means | Example |
|---|---|---|
| Area | Every place is the right size compared with others | Equal Earth, Gall-Peters |
| Shape (in small areas) and direction | Small places look right; compass courses are straight lines | Mercator |
| A little of everything | Nothing is exact, nothing is far off | Robinson, Winkel tripel |
Worked example: Where is the stretch?
On the left map above, Greenland looks about as big as Africa. On the right map it looks much smaller. Which map is lying?
- Both maps show the same countries; only the projection differs.
- Greenland is far from the equator, where the left map (Mercator) stretches things most.
- The right map (Equal Earth) keeps areas true, so its sizes can be compared.
Answer: The left map exaggerates Greenland. On the globe, Africa is about 14 times larger.
Common mistake
Thinking one flat map is the "correct" one and the others are wrong. Every projection is a trade-off. Ask what a map is for, then pick the projection that keeps the right thing true. And when sizes matter, compare on a globe or an equal-area map.