The Map Reading Handbook
Every projection is a bargain: to draw a round Earth on flat paper, the mapmaker chooses which truths to keep and which to let go.
Start with the peel. A globe can be sliced and pressed flat only if the skin stretches or tears; a projection is the mathematics that decides where the stretching goes. The three classic developable surfaces — the cylinder, the cone and the plane — are wrapped around or touched to the globe, the graticule is transferred, and the surface is unrolled.
Four properties are traded in this transfer. Shape means local angles are kept, so a coastline's wiggles look right at small scales. Area means regions keep their true relative size. Distance means lengths from a point or along a line stay true. Direction means bearings from a point are correct. A single projection can honour at most a couple of these across the whole sheet.
Mercator's cylindrical projection of 1569 chose angles: any straight line on it is a line of constant compass bearing, which made it priceless for sailors. The price is area — inflation grows with latitude until polar lands balloon. Greenland, on such a map, rivals Africa; in truth Africa is roughly fourteen times larger.
On narrow screens, swipe or scroll the plate sideways.
Equal-area projections such as the Mollweide or the Gall–Peters choose size instead: countries keep their proportions, but their shapes stretch and shear. Compromise projections, like the Robinson, keep nothing exactly and everything tolerably, which is why they please the eye in atlases.
The reader's instrument for seeing all this is Tissot's indicatrix: imagine tiny identical circles scattered over the globe, then look at what the projection did to them. Where the circles stay round, shape is kept; where they stay the same size, area is kept; where they stretch into ellipses, something was spent.
The habit to keep: before comparing two distant places on any world map, ask which projection drew it. The question costs a second and prevents the most common misreading in all of cartography.
Further reading