Map projection

Lore & Background

In cartography, a map projection is any of a broad set of transformations employed to represent the curved two-dimensional surface of a globe on a plane. Coordinates, often expressed as latitude and longitude, of locations from the surface of the globe are transformed to coordinates on a plane. Projection is a necessary step in creating a two-dimensional map and is one of the essential elements of cartography. All projections of a sphere on a plane necessarily distort the surface in some way. Depending on the purpose of the map, some distortions are acceptable and others are not; therefore, different map projections exist in order to preserve some properties of the sphere-like body at the expense of other properties. The study of map projections is primarily about the characterization of their distortions. There is no limit to the number of possible map projections.

Reader's Guide

Map projections are fundamental to cartography because they enable the representation of the Earth's curved surface on a flat map, a necessary step for navigation, planning, and geographic analysis. The most well-known map projection is the Mercator projection, which is conformal but has been criticized for enlarging regions further from the equator. Equal-area projections, such as the Sinusoidal and Gall–Peters projections, show correct relative sizes of countries but distort angles. The National Geographic Society and most atlases favor compromise projections like the Robinson and Winkel tripel that balance area and angular distortion. Carl Friedrich Gauss's Theorema Egregium proved that a sphere's surface cannot be represented on a plane without distortion. The classical way of showing distortion is Tissot's indicatrix, which illustrates the amount and orientation of distortion components. The creation of a map projection involves selecting a model for the shape of the Earth (sphere or ellipsoid) and transforming geographic coordinates to plane coordinates. Projections can be literal (like casting a shadow) or any mathematical function that transforms coordinates smoothly. The choice of projection depends on the map's purpose and compatibility with data sets.

Did You Know?

• All projections of a sphere on a plane necessarily distort the surface in some way.
• The most well-known map projection is the Mercator projection, which is conformal.
• Carl Friedrich Gauss's Theorema Egregium proved that a sphere's surface cannot be represented on a plane without distortion.
• The classical way of showing distortion is Tissot's indicatrix.

The Unavoidable Geometry Problem

The fundamental challenge of mapping the entire Earth onto a flat surface is one of geometry. Because the planet is three-dimensional, any two-dimensional rendering must distort the display of its surface. While some degree of distortion is inherent in any map, world maps push these distortions to their extremes due to their scale. Over the centuries, cartographers have developed numerous projection techniques, each representing a different method of translating a globe onto a plane. Every single one of these projections distorts geographic features, distances, and directions to some degree. The various methods that have been created essentially offer different strategies for balancing accuracy against the unavoidable distortion that comes with rendering a sphere on a flat sheet. Perhaps the most famous example is the Mercator Projection, which was originally conceived as a nautical chart rather than a general-purpose depiction of the world. The choice of projection is never neutral; it determines what the map emphasizes and what it sacrifices in the process.

From Myth to Measurement: The Long Road to a Complete Map

Creating an accurate world map demands global knowledge of Earth's oceans and continents, a knowledge that accumulated over millennia. From prehistory through the Middle Ages, producing a truly accurate world map was simply impossible, since no single culture had knowledge of more than half of Earth's coastlines, and only a tiny fraction of continental interiors was understood by anyone. The European Renaissance marked a turning point, as exploration began to rapidly expand humanity's understanding of the planet's surface. By the mid-1700s, most of the world's coastlines had been charted, at least in rough outline. It was not until the twentieth century that the vast interior regions of the continents were finally mapped. This long progression means that early world maps tell us as much about what people believed and imagined as they do about actual geography, reflecting the philosophical and cultural frameworks of their era rather than modern scientific precision.

Many Kinds of World Maps

World maps are not a single uniform product; they serve a wide range of technical and aesthetic purposes. Political maps highlight territorial boundaries and patterns of human settlement, making them tools for understanding governance and borders. Physical maps shift the focus to natural geographical features such as mountain ranges, soil types, and land-use patterns. Geological maps go even deeper, revealing not just the surface but the characteristics of underlying rock, fault lines, and subsurface structures. Choropleth maps take a different approach entirely, using variations in color hue and intensity to contrast differences between regions, often to display demographic or economic statistics. Thematic maps, a closely related category, concentrate on one or a few focused subjects and can portray physical, social, political, cultural, economic, sociological, or agricultural aspects of any geographic area from a single city to an entire continent. The choice of map type determines which story the surface of the Earth is made to tell.

Maps as Cultural Artifacts and Vehicles of Ideas

World maps have always been more than practical tools; they are cultural documents that reflect the worldview of the people who create them. Early maps, spanning from the Iron Age through the Age of Discovery and into the emergence of modern geography during the early modern period, often embodied philosophical and cultural assumptions that were radically different from those underlying contemporary cartography. These historical maps provide valuable information not only about which places were known at various points in time but also about the intellectual frameworks that shaped how people understood their world. Maps serve as one of the key means by which scientists and thinkers distribute their ideas and pass them on to future generations. The persistence of certain traditions alongside transformation, visible in the evolution from medieval to Renaissance cartography, shows that mapping is as much an act of interpretation as one of measurement, carrying forward ideas across centuries.