Projections

History of Maps and Cartography

Course 1 · Chapter 5 · Mercator and Map Projections

A sphere cannot be flattened without stretching, tearing or squashing something, a fact proved in the nineteenth century by Gauss (check). Every flat map of the world is therefore a compromise, and a projection is a rule for choosing which distortions to accept. This chapter explains what Mercator's famous map was designed to do, what its critics say, and how other projections trade one kind of accuracy for another. Names and dates are from general knowledge and flagged "check".

The Problem

Orange peel

Peel an orange and try to press the skin flat: it splits or stretches. A map projection is a mathematical way of doing the same job with rules.

Four properties

A projection can try to keep shape (locally), area, distance or direction, but no flat map keeps all of them for the whole world (check).

Three families

Maps can be projected as if onto a cylinder, a cone or a flat plane. The shape of the surface and where it touches the globe decide where the distortion is smallest (check).

Mercator's Projection

Date. Gerard Mercator published his world map in 1569 (check).
The aim. A line of constant compass bearing, a rhumb line, appears as a straight line, which helps a navigator plot a course with a ruler and a compass (check).
The cost. Areas grow larger towards the poles. Greenland looks as large as Africa, though Africa is about fourteen times larger (check the ratio).
The use. It is a navigator's chart, and was never designed as a wall map of the world's countries, though that is how it was used for centuries.
Web maps. A close relative, Web Mercator, is used by many online maps, because it keeps shapes right at city scale (check; Chapter 9).

Projection (check each)	Keeps	Distorts
Mercator, 1569	Local shapes and compass bearings	Area, strongly near the poles
Gall–Peters (equal-area), 1855 and 1973	Area	Shape; countries look stretched near the equator
Mollweide, 1805	Area	Shape near the edges
Robinson, 1963	A pleasing look, a compromise	Everything a little; not strictly equal area or conformal
Winkel tripel, 1921	A compromise of area, distance and angle	Everything a little; adopted by National Geographic in 1998
Azimuthal equidistant	Distances and directions from the centre point	Shape and area far from the centre

The Peters argument In 1973 Arno Peters presented an equal-area map as a fairer picture of the world, and argued that Mercator's maps had favoured Europe. The projection had been described earlier by James Gall (check). Map scholars criticised the claims of novelty, and the stretched shape. The argument is useful because both sides were right about something: area matters for fair comparison, and no projection is neutral.

Choosing a Projection

Task	A sensible choice (check)
Plotting a compass course	Mercator
Comparing areas, such as population density	An equal-area projection
A general wall map	A compromise projection such as Winkel tripel
Flight routes	A globe, or a map in which great circles appear straight, such as a gnomonic projection
Local survey maps	A projection fitted to the region, such as the Transverse Mercator on which the British National Grid is based

A British comparison The Ordnance Survey uses a Transverse Mercator projection for the British National Grid, which is why a grid reference such as NT 25 73 gives a position on every OS map (check the example). A projection chosen for one small region distorts little there, and would distort badly if stretched across the world.

Check the details Claims that a projection "is wrong" or "tells the truth" need to say for which purpose. Check numbers such as area ratios and the dates and attributions of projections before quoting them.

Exercises

Exercise 1

Explain why Greenland looks so large on a Mercator map, and what Mercator's design was meant to achieve.

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Exercise 2

Choose a projection for each of three tasks (a sailing course, a map of population density, a wall map for a school) and give a reason.

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Exercise 3

Use an orange peel, a globe or a free online tool that compares projections, and write three observations about distortion.

→ Solution

Quick Reference

No perfect map: a sphere cannot be flattened without distortion
Mercator: straight compass lines, inflated polar areas
Equal-area: true size, stretched shape
Compromise: Robinson, Winkel tripel
Rule: choose the projection to fit the task