The Mercator Map
Africa is fourteen times larger than Greenland, but they look similar in size on a Mercator map. Model how map distortion grows with latitude.
Where this idea comes from
Start here — these are the sources that inspired this exploration.
Introduction
On the Mercator projection, Greenland looks almost the same size as Africa. In reality, Africa is about 30.3 million km2, more than fourteen times the area of Greenland's 2.1 million km2 - you could fit the U.S. (9.8 million km2), China, India and most of Europe inside Africa and still have room left. On a globe the true proportions are clear, but the Mercator projection stretches land more and more as you move away from the equator, so high-latitude regions look far larger than they are. Modelling the exact scale factor requires calculus beyond standard DP content, so this exploration builds an empirical model instead: measure the distortion at several latitudes and fit a function to it.
Guiding Questions
- Why can't a sphere be flattened onto a map without distortion?
- How does the Mercator projection stretch distances as you move away from the equator?
- Compare the map area of Greenland and Africa with their true areas. How big is the distortion, and can you model it with a function of latitude?
- Which other projection could you compare it with, and how would you measure which one is 'fairer'?