Maps, Scale, and the Cost of Every Projection

Why every map lies a little

A map is a flat representation of a curved Earth. That transfer cannot be done without loss: a projection can preserve shape, area, distance, or direction, but never all four at once. The exam question is almost never "which projection is correct" — it is which distortion is acceptable for this purpose.

Mercator is conformal: local shapes and compass bearings are true, which is why sailors used it. The price is area — landmasses near the poles are inflated enormously. Gall-Peters is equal-area: relative sizes are honest, but shapes are stretched. Robinson is a compromise: it distorts everything slightly and nothing badly. An azimuthal projection keeps true direction and distance from a single centre point, which is why it suits flight paths and polar views.

Scale, in two senses

Cartographic scale is the ratio between map distance and ground distance. It is written three ways: as a fraction or ratio (1:24,000), as a written statement ("one inch to 2,000 feet"), or as a graphic bar — and only the bar stays correct when the map is enlarged or shrunk.

A large-scale map covers a small area in great detail; a small-scale map covers a large area with little detail. Students reverse this constantly. Read the fraction: 1/24,000 is a larger number than 1/1,000,000, so 1:24,000 is the large-scale map.

Kinds of maps

Reference maps (political, physical, road) show where things are. Thematic maps show a pattern of one variable: choropleth (shaded by rate), dot distribution (one dot equals n occurrences), graduated symbol (symbol size scales with value), isoline (lines joining equal values), and cartogram (area redrawn in proportion to the variable itself).