Reading maps: scale, projection and coordinates

A map is a simplified model of a place. It leaves out most details to show the ones that matter for its purpose, whether that is roads, rainfall, population or borders. Every map is a set of choices made by its maker.

People have made maps for thousands of years. A Babylonian clay tablet from around the sixth century BCE shows the world as a disc surrounded by water, and Greek scholars such as Eratosthenes estimated the circumference of the Earth remarkably accurately in the third century BCE.

Lines of latitude run east to west around the globe and measure distance north or south of the equator, from 0 degrees at the equator to 90 degrees at each pole. Lines of longitude, or meridians, run from pole to pole and measure distance east or west of the prime meridian at Greenwich in London, up to 180 degrees.

Together they give every place a unique address. The Eiffel Tower, for example, lies at about 48.86 degrees north and 2.29 degrees east. Finding latitude at sea was relatively easy using the sun or stars, but finding longitude required knowing the exact time at a reference point, a problem solved in the eighteenth century by John Harrison's accurate marine chronometers.

Scale tells you how distance on the map relates to distance on the ground. A scale of 1:50,000 means one centimetre on the map equals 50,000 centimetres, or half a kilometre, in reality.

A large-scale map, such as 1:10,000, shows a small area in great detail, like a town plan. A small-scale map, such as 1:10,000,000, shows a large area with little detail, like a map of a continent. The names can be confusing, but the rule is that a larger fraction means a more zoomed-in map.

You cannot flatten the surface of a sphere without stretching or tearing it, as anyone who has tried to flatten an orange peel knows. A map projection is a mathematical method for transferring the curved surface onto a flat one, and every projection distorts at least one of area, shape, distance or direction.

The Mercator projection, created in 1569, keeps angles correct, which made it invaluable for navigation because a straight line on the map is a constant compass bearing. But it greatly enlarges areas near the poles. Greenland looks about the size of Africa, while Africa is actually around fourteen times larger.

• Mercator: preserves angles, used for navigation and web maps, but distorts area severely near the poles.
• Equal-area projections, such as the Gall-Peters or Mollweide: show true relative sizes but distort shapes.
• Robinson and Winkel tripel: compromises that look balanced, often used for world maps in atlases.
• Azimuthal projections: show true directions from a central point, useful for radio and air routes.

Topographic maps show the shape of the land using contour lines, which join points of equal height. Contours close together mean steep ground; widely spaced contours mean gentle slopes. A set of closed rings marks a hill or summit.

Maps also use symbols, colours and a legend to show features such as rivers, forests, churches and footpaths. Modern digital maps combine satellite images, GPS and geographic information systems, which layer many kinds of data on the same map, but the core ideas of scale, projection and coordinates remain the same.