Map projections are ways to represent Earth’s curved surface on a flat map. They matter because every flat world map changes some combination of shape, area, distance, or direction. A globe can show these features naturally, but it is hard to print, measure, or display in a rectangular screen format.
A projection is a mathematical compromise between accuracy and usefulness.
Understanding Geometry: Map Projections
A projection begins with positions on Earth described by latitude and longitude. Mathematics converts each position into a location on a sheet or screen. Imagine placing a transparent surface around a globe, marking points onto it, then opening that surface out.
A cylinder can touch the globe at the equator or cut through it at two lines. A cone can touch near one latitude or cross the globe along two arcs. A flat plane can touch at one point.
The places where the surface touches or cuts the globe have the least stretching. Distortion usually increases farther away from those places.
The pattern of grid lines gives useful clues about a map. Meridians are lines running from pole to pole. Parallels run around Earth east to west.
On a globe, meridians meet at the poles and parallels stay evenly spaced according to their north to south separation. A projection may draw these lines straight, curved, equally spaced, or increasingly far apart. Those choices reveal what the map was designed to preserve.
On many navigation maps, a straight line can represent a constant compass bearing. This helps a ship or aircraft hold one direction, though the route may not be the shortest path on Earth.
The shortest surface route between two places usually follows part of a great circle. A great circle is made by slicing a sphere through its center. The equator is one example.
Most long airplane routes are close to great circle routes. On a flat world map, such routes often look curved, especially at high latitudes. This can make a route over the Arctic seem surprising even when it saves distance.
For local measurements, mapmakers use a scale factor. It compares a small map length with the matching ground length near one location. Students should remember that a scale bar may be accurate only in certain parts of a world map.
Different tasks need different maps. A teacher comparing the sizes of countries needs a projection that treats area fairly. A pilot planning a long route needs reliable directions and distances for the region involved.
A city engineer needs a local projection that keeps streets, property boundaries, and measured lengths close to reality. Digital maps add another complication. A phone map changes scale as a user zooms, and its projection may make nearby features easy to read while giving a misleading impression of the whole planet.
When studying a map, check its title, legend, projection name, standard lines, and scale information. Notice which regions look stretched. That habit turns a map from a picture into evidence that can be judged carefully.
Key Facts
- A sphere cannot be flattened into a plane without distortion in shape, area, distance, or direction.
- Mercator projection preserves local angles and directions, so it is conformal, but it greatly enlarges areas near the poles.
- Equal-area projections preserve relative area, so equal regions on Earth have equal areas on the map, but shapes may be stretched.
- Robinson projection is a compromise projection that balances shape and area distortion for a visually pleasing world map.
- Map scale is local on most projections: scale factor = map distance / globe distance at that location.
- On Earth, distance along a meridian is approximately d = Rθ, where R is Earth’s radius and θ is the central angle in radians.
Vocabulary
- Map projection
- A map projection is a mathematical method for transforming locations on a curved surface into locations on a flat plane.
- Distortion
- Distortion is the change in size, shape, distance, or direction that occurs when a curved surface is shown on a flat map.
- Mercator projection
- The Mercator projection is a conformal cylindrical projection that preserves local angles but exaggerates area near the poles.
- Equal-area projection
- An equal-area projection preserves the relative sizes of regions even though it may distort their shapes.
- Tissot indicatrix
- A Tissot indicatrix is a small circle drawn on a globe that becomes an ellipse on a map to show local distortion.
Common Mistakes to Avoid
- Treating a flat world map as if all areas are accurate. This is wrong because projections like Mercator enlarge high-latitude regions such as Greenland and Antarctica.
- Assuming one projection is best for every purpose. This is wrong because navigation, area comparison, classroom display, and local surveying require different preserved properties.
- Measuring long straight-line distances on any world map without checking the projection. This is wrong because a straight line on a flat map may not represent the shortest path on the globe.
- Thinking latitude and longitude grid squares have the same real size everywhere. This is wrong because meridians meet at the poles, so grid cells shrink in real area as latitude increases.
Practice Questions
- 1 On a globe with radius 6370 km, two cities lie on the same meridian and differ in latitude by 12 degrees. Estimate the north-south distance between them using d = Rθ, with θ in radians.
- 2 On a map, the distance between two cities is 8.0 cm. The local scale is 1 cm = 250 km. What is the real-world distance between the cities?
- 3 A student wants to compare the land area of countries near the equator with countries near the Arctic. Should the student choose Mercator, Robinson, or an equal-area projection, and why?