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Cartographers have known for centuries that Mercator isn’t an especially accurate way of viewing the world, and they’ve developed a number of mathematical tools for projecting the earth’s spherical surface onto a two-dimensional map. But there’s no such thing as a perfect map projection! Every projection has its advantages and disadvantages. To understand why, we have to venture back into mathematics.

Properties of map projections

Let’s consider what an ideal map would look like.

First, the map should be contiguous — there shouldn’t be any interruptions in it. Just as any two points on the earth’s surface can be connected by a line, someone should be able to draw a line between any two points on the map. We don’t, in other words, want something like this:

Figure 9-1. A Goode-Homolosine projection, shown interrupted to preserve the position of the continents.

Interrupted map of the globe

For the remainder of this discussion we’re going to consider only contiguous maps — maps that preserve the topological characteristics we talked about before.

In drawing these maps, there are four properties of the earth’s surface we’d like to preserve.

Area
The areas of regions on the map should be proportional to their areas on the earth’s surface. Maps that preserve relative areas of regions are called equal-area maps.
Distance
Distances between points on the map should be proportional to the distances between those points on the earth’s surface. Maps that preserve distance are called equidistant maps.
Direction
Directions from the center of the map to various points on the map should be shown correctly. Maps that do this are called azimuthal maps.
Shape
Shapes of regions should be drawn correctly, which means we have to preserve local angles — all angles at any point are preserved, the scale at any point is the same in every direction, and lines of latitude and longitude intersect at right angles. Maps that do this are called conformal maps.

The problem is that achieving all four of these properties on a two-dimensional map is impossible. Mathematicians have proven this. Preserving any one requires distorting at least one other.

This table shows which properties can be combined in a single map projection:

Figure 8-2. Properties that can be combined in a single map projection.

Equal-Area Equidistant Azimuthal Conformal
Equal-Area no yes no
Equidistant no yes no
Azimuthal yes yes yes
Conformal no no yes

Types of projections

Mapmakers and mathematicians have invented dozens of map projections — the possibilities are almost limitless. As new needs arise — such as the need to project satellite imagery onto a computer screen with minimal distortion — new projections are invented.

Most projections fall into a few basic categories:

Cylindrical

Cylindrical projections unwrap the earth’s surface and project it onto the surface of a cylinder. The Mercator projection is cylindrical, as are several variations on it.

Figure 9-3. The Mercator projection projects the earth’s spherical surface onto a cylinder. Courtesy U.S. Geological Survey.

Mercator projection

Conic

In a conic projection, the earth’s surface is mathematically projected onto a cone.

Figure 9-4. The Albers Equal Area Conic projection projection projects the earth’s spherical surface onto a cone. Courtesy U.S. Geological Survey.

Albers Equal Area Conic projection

Azimuthal

An azimuthal projection geometrically maps the earth’s surface onto a plane.

Figure 9-5. The orthographic projection projects the earth’s spherical surface onto a plane. Courtesy U.S. Geological Survey.

orthographic projection

Properties of common projections

The U.S. Geological Survey provides an overview of several common map projections, with an explanation of how each is created and what it’s most useful for. The table below summarizes the properties of common map projections.

Figure 9-6. Properties of various map projections. Adapted from the U.S. Geological Survey. Click the name of a projection to get more information about it.

Key:
yes yes
partly partly

Projection Type Conformal Equal area Equidistant Azimuthal (true direction)
Globe Sphere yes yes yes yes
Mercator Cylindrical yes     partly
Transverse Mercator Cylindrical yes      
Oblique Mercator Cylindrical yes      
Space Oblique Mercator Cylindrical yes      
Miller Cylindrical Cylindrical        
Robinson Pseudo-cylindrical        
Sinusoidal Equal Area Pseudo-cylindrical   yes partly  
Orthographic Azimuthal       partly
Stereographic Azimuthal yes     partly
Gnomonic Azimuthal       partly
Azimuthal Equidistant Azimuthal     partly partly
Lambert Azimuthal Equal Area Azimuthal   yes   partly
Albers Equal Area Conic Conic   yes    
Lambert Conformal Conic Conic yes     partly
Equidistant Conic Conic     partly  
Polyconic Conic     partly  
Bipolar Oblique Conic Conformal Conic yes      

Choosing a projection

Finally, this table gives a summary of what kinds of maps each projection is more and less suitable for.

Figure 9-7. Suitability of various projections to mapping purposes. Adapted from the U.S. Geological Survey. Click the name of a projection to get more information about it.

Key:
yes yes
partly partly

Projection Type World Hemisphere Continent/
Ocean
Region/
sea
Medium scale Large scale
Globe Sphere yes          
Mercator Cylindrical partly     yes    
Transverse Mercator Cylindrical     yes yes yes yes
Oblique Mercator Cylindrical     yes yes yes yes
Space Oblique Mercator Cylindrical           yes
Miller Cylindrical Cylindrical yes          
Robinson Pseudo-
cylindrical
yes          
Sinusoidal Equal Area Pseudo-
cylindrical
yes   yes      
Orthographic Azimuthal   partly        
Stereographic Azimuthal   yes yes yes yes yes
Gnomonic Azimuthal       partly    
Azimuthal Equidistant Azimuthal partly yes yes yes   partly
Lambert Azimuthal Equal Area Azimuthal   yes yes yes    
Albers Equal Area Conic Conic     yes yes yes  
Lambert Conformal Conic Conic     yes yes yes yes
Equidistant Conic Conic     yes yes    
Polyconic Conic         partly partly
Bipolar Oblique Conic Conformal Conic     yes