Map projection
Mathematical transformation of a globe's surface onto a plane.
A map projection is a mathematical transformation used in cartography to represent the curved two-dimensional surface of a globe on a plane. It 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, and different projections exist to preserve some properties at the expense of others.
- field
- Cartography
- known_for
- Transforming coordinates from a curved surface to a plane for mapmaking
Lore & Background
In cartography, a map projection transforms coordinates, often expressed as latitude and longitude, from the surface of the globe 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.
Reader's Guide
Map projections are fundamental to cartography because they allow the representation of the Earth's curved surface on a flat map. The study of map projections is primarily about the characterization of their distortions, as all projections distort due to the Theorema Egregium, which proved that a sphere's surface cannot be represented on a plane without distortion. Different projections preserve different metric properties such as area, shape, direction, bearing, or distance. For example, the Mercator projection is conformal but enlarges regions further from the equator, while equal-area projections like the Sinusoidal and Gall–Peters projections show correct sizes but distort angles. The National Geographic Society and most atlases favor compromise projections like the Robinson and Winkel tripel. The choice of projection depends on the map's purpose and compatibility with data sets, as different datums assign slightly different coordinates to the same location. Distortion is often visualized using Tissot's indicatrix, which shows the amount and orientation of distortion at points across the map.
Did You Know?
- The term 'map projection' is not limited to perspective projections; any mathematical function that transforms coordinates from the curved surface distinctly and smoothly to the plane is a projection.
- Few projections in practical use are perspective projections.
- 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.
Frequently Asked Questions
What is a map projection?
A map projection is the mathematical process of converting coordinates from the curved surface of a globe onto a flat, two-dimensional plane. It is the essential first step cartographers take whenever they need to render a spherical world as a usable flat map.
Why can't a globe be flattened without any distortion?
A sphere's surface geometry simply cannot be unfolded onto a plane without some stretching, tearing, or compression. Every projection must therefore sacrifice at least one property—shape, area, distance, or direction—while trying to keep others as accurate as possible.
What field does map projection belong to?
Map projection sits squarely within cartography, the broader discipline of mapmaking. It is one of the core mathematical tools that makes the creation of any two-dimensional map possible.
Can different projections be chosen for different purposes?
Yes—cartographers select a specific projection depending on which property they need to protect, such as preserving angles for navigation or maintaining true areas for thematic maps. No single projection is universally best because each one trades off different kinds of distortion.
What is the practical role of a map projection in mapmaking?
It acts as the coordinate-transformation engine that takes every point on the curved Earth and assigns it a corresponding position on a flat sheet. Without this step, there would be no way to produce a usable two-dimensional map from real-world geography.
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