Maps are fundamental tools we use every day to navigate our world, visualize data, and understand geography.
From planning a road trip to studying global climate patterns, maps provide an indispensable visual representation of our planet.
However, anyone who has looked at a few different maps of the world will quickly notice something peculiar: they don't all look the same.
Continents can appear vastly different in size relative to each other, shapes might be stretched or squashed, and the overall layout can vary dramatically.
This isn't arbitrary; it's a direct consequence of something called map projection.
The main point relevant to anyone who uses or creates maps is this: representing our spherical Earth on a flat surface—a map—is mathematically impossible without introducing errors, or distortions.
Understanding these distortions is key to interpreting any map correctly and appreciating why cartographers have developed hundreds, if not thousands, of different map projections.
This post will delve into the fundamental challenge of mapping the Earth, explore the specific types of distortion that occur, and most importantly, explain *why* different projections exist, offering a solution to the confusion by empowering you to understand the compromises inherent in every flat map.
Imagine trying to flatten an orange peel perfectly onto a table without tearing or stretching it.
You simply cannot do it.
The peel, like the Earth's surface (which is closer to a geoid, but for mapping purposes, we often think of it as a sphere or ellipsoid), has a curved, three-dimensional surface.
A map, on the other hand, is a flat, two-dimensional representation.
The act of transforming a 3D surface into a 2D plane is what a map projection does, and it is this transformation that makes distortion unavoidable.
This isn't a flaw in cartography; it's a mathematical certainty.
Every projection is a systematic method of translating points from the curved surface of the Earth to corresponding points on a flat surface.
This translation involves mathematical formulas that necessarily stretch, compress, or tear the surface in different ways and in different places.
Understanding this core principle—that you cannot have a perfectly accurate flat map of the Earth—is the first step to understanding why different projections exist and what compromises each one makes.
When the Earth's 3D surface is projected onto a 2D map, four fundamental properties of geographic features can be distorted:
Area, Shape, Distance, and Direction.
A single map projection cannot preserve all four of these properties simultaneously across the entire map.
In fact, typically, a projection can only preserve one or two properties perfectly, or none at all, opting instead to balance the distortions of multiple properties.
Understanding these four types of distortion is crucial because different map projections prioritize preserving different properties, depending on the map's intended use.
An equal-area or equivalent projection is one that preserves the relative sizes of areas.
This means that on the map, the area of any geographic feature is proportional to its actual area on the Earth's surface.
For example, if Brazil is actually about the same size as Australia, an equal-area map will show them with roughly the same area on the map.
When area is *not* preserved (i.e., on non-equal-area maps), continents or countries can appear much larger or smaller than they are in reality, especially those located far from the projection's standard lines or points.
This distortion is often the most visually striking and can lead to significant misperceptions about the true size and importance of regions, as seen in the famous Mercator projection where Greenland looks massive compared to Africa, when in reality Africa is fourteen times larger.
A conformal projection is one that preserves the shape of small areas, meaning that the angles between intersecting lines (like coastlines and meridians) are preserved correctly at any point on the map.
This results in features like coastlines and continents appearing with their correct local shapes.
Another characteristic of conformal maps is that lines of latitude and longitude intersect at right angles, just as they do on a globe.
However, shape preservation on a flat map is only truly accurate for *small* areas; the shape of very large regions, like entire continents, will still be distorted, although they may look familiar due to the local accuracy.
The trade-off for preserving shape is significant distortion in area, especially as you move away from the points or lines where the projection touches the globe (standard parallels or central meridian).
An equidistant projection is one that preserves true scale along certain lines.
This means that distances measured along these specific lines on the map are proportional to the true distances on the Earth's surface.
Crucially, no flat map can be equidistant *everywhere* and in *all* directions simultaneously.
Equidistant projections are typically only true-to-scale from one or two points, or along specific lines (like all meridians or specific parallels).
If a map is equidistant from a central point, you can measure the distance from that point to any other point on the map accurately.
However, distances between two points, neither of which is the central point, will likely be incorrect.
An azimuthal or true-direction projection is one that preserves the true direction or azimuth from a single point on the map to any other point.
This means that a straight line drawn from the central point of the projection to any other point on the map represents the correct geographic direction (the shortest path, a great circle route) from the center.
Like equidistant projections, azimuthal projections are typically only true for directions originating from the central point.
Directions between two points, neither of which is the center, are generally not accurate.
These projections are particularly useful for applications where knowing the true bearing from a specific location (like a radio tower or an airport hub) is important.
While the actual mathematical formulas for map projections can be complex, many projections can be conceptualized by imagining projecting the Earth's surface onto a simple geometric shape that can be flattened.
These shapes are typically a cylinder, a cone, or a plane (tangent to a single point).
Cylindrical projections, like the Mercator, are conceptually created by wrapping a cylinder around the globe (often tangent at the equator), projecting the surface onto the cylinder, and then unrolling it.
These projections often result in rectangular maps and can have significant distortion near the poles.
Conical projections, like the Albers or Lambert Conformal Conic, are imagined by placing a cone over the globe (often touching at one or two standard parallels), projecting the surface onto the cone, and then unrolling it.
These are commonly used for mapping regions that are mainly east-west in extent, like the contiguous United States.
Planar or Azimuthal projections are created by placing a flat plane tangent to the globe at a single point (or sometimes cutting through it).
Projecting the globe onto this plane results in a circular map, centered on the tangent point.
These projections are often used for polar maps or for showing airline routes radiating from a hub airport.
Many modern projections are not based on simple geometric shapes but are complex mathematical constructions designed to optimize certain properties or minimize overall distortion in a particular region or for a specific purpose.
Understanding these basic conceptual models helps explain why different projections have characteristic patterns of distortion—cylindrical maps often stretch poles horizontally, conical maps show curved meridians, and planar maps radiate from a central point.
Since no single flat map can preserve Area, Shape, Distance, *and* Direction everywhere, the fundamental reason why so many different map projections exist is that different maps serve different purposes.
A cartographer choosing a projection must decide which properties are most important for the map's intended use and which distortions are acceptable trade-offs.
For example, a map designed for marine navigation needs to preserve angles accurately so that a constant compass bearing appears as a straight line.
Shape preservation is crucial for this, even if area is severely distorted, which leads cartographers to choose a conformal projection like the Mercator.
On the other hand, a map showing the distribution of populations or natural resources needs to accurately represent the size of landmasses so that visual comparisons of density or total amounts are not misleading.
For this purpose, an equal-area projection is essential, even if the shapes of countries appear somewhat distorted.
Similarly, maps used for radio broadcasting might prioritize preserving true direction from the broadcast tower (an azimuthal projection), while maps for route planning from a specific location might prioritize true distance from that point (an equidistant projection).
Some projections are designed not to preserve any single property perfectly but to minimize the overall distortion across the entire map, attempting to strike a balance between area, shape, and distance distortions.
These "compromise" projections are often used for general reference world maps found in atlases or wall hangings, where a visually appealing representation that doesn't too severely distort any single property is desired.
The sheer variety of map projections available reflects the diverse ways we use maps and the need to tailor the projection to the specific task at hand, prioritizing the properties most critical for that task.
Let's look at some common and significant map projections to understand how their design leads to specific types of distortion and makes them suitable for particular applications.
The Mercator projection, developed by Gerardus Mercator in 1569, is perhaps the most famous and also one of the most controversial map projections.
Primary preserved property: Shape (Conformal).
Major distortion: Area. Distortion increases dramatically with distance from the equator.
Common use: Historically, marine navigation (rhumb lines or loxodromes, lines of constant compass bearing, are straight lines on the map). Also used in many online web mapping services (often a variation called Web Mercator).
Quirks and criticisms: Due to its conformal nature, the Mercator preserves angles and local shapes, making it excellent for sailing where maintaining a constant compass direction is key.
However, its area distortion is severe; Greenland appears larger than Africa, when in reality Africa is 14 times larger.
Alaska looks bigger than Brazil, but Brazil is five times its size.
This visual misrepresentation of relative size has led to criticisms regarding its use in general reference maps, as it can create a distorted sense of geopolitical scale, often exaggerating the size of countries in higher latitudes (Europe, North America) relative to those nearer the equator (Africa, South America).
When accurately comparing the sizes of different landmasses or representing thematic data like population density or resource distribution, equal-area projections are essential.
Primary preserved property: Area (Equivalent).
Major distortion: Shape and Distance. Shapes are typically compressed in one direction and stretched in the perpendicular direction; distances are generally incorrect except along specific lines.
Common uses: Thematic mapping, atlases showing relative sizes, resource distribution maps, population maps.
Examples:
1. The Gall-Peters Projection (or Peters Projection):
Developed by James Gall in the 19th century and later popularized by Arno Peters in the 20th century.
Known for its rectangular shape and pole-to-pole coverage.
It stirred significant debate as an alternative to the Mercator, promoted for its equal-area property which proponents argued offered a more equitable view of the world, particularly highlighting the true sizes of developing nations in the Southern Hemisphere relative to developed nations in the Northern Hemisphere.
Its shapes are noticeably distorted, particularly near the poles and the equator.
2. The Albers Equal-Area Conic Projection:
A conic projection commonly used for maps of regions with a predominant east-west extent, such as the United States.
It is an equal-area projection.
Shapes and distances are reasonably accurate along the two standard parallels where the cone conceptually intersects the globe, but distortions increase away from these parallels.
While no world map can show true distances between *all* pairs of points, equidistant projections maintain accurate scale along specific paths.
Primary preserved property: Distance (along specific lines).
Major distortion: Area, Shape, and often Direction (except from the point or along the line of true scale).
Common uses: Airline route maps from a hub, radio propagation maps, maps for measuring distances from a specific location (e.g., emergency response maps from a station).
Example:
1. The Azimuthal Equidistant Projection:
An azimuthal projection centered on a specific point.
Distances measured along any straight line radiating from the central point are true to scale.
Directions from the central point are also true (it's also azimuthal).
Shapes and areas are distorted, particularly as you move away from the center.
Often used for world maps centered on a major city or pole, showing how far away other locations are along a straight line path from that center.
Azimuthal projections are valuable when the crucial information is the true compass direction from a specific point.
Primary preserved property: Direction (from a central point).
Major distortion: Area, Shape, and typically Distance (except sometimes along lines radiating from the center, if it's also equidistant).
Common uses: Aeronautical and marine charts showing bearings, maps for plotting great circle routes (shortest path between two points on a sphere), polar maps.
Example:
1. The Gnomonic Projection:
An azimuthal projection where the projection point is the center of the globe.
The defining characteristic is that all great circles (the shortest paths between any two points on the globe, like segments of longitude lines or the equator) are shown as straight lines.
This makes it invaluable for plotting ship or aircraft courses, as navigating along a straight line on a gnomonic chart means following a great circle route.
Area and shape distortions are severe, especially away from the center point.
For general reference maps, where no single property is paramount but a visually appealing and reasonably balanced representation of the entire world is desired, compromise projections are often used.
These projections do not preserve any property perfectly across the entire map but distribute and minimize the distortions in Area, Shape, Distance, and Direction to achieve a more aesthetically pleasing and less misleading overall appearance for a world map.
Primary preserved property: None perfectly, but seeks to minimize multiple distortions.
Major distortion: All four properties are distorted, but ideally less severely than on projections that preserve one property perfectly.
Common uses: World atlases, wall maps, general geography illustrations.
Examples:
1. The Robinson Projection:
Developed in 1963, it was widely adopted by the National Geographic Society for world maps from 1988 to 1998.
It is not based on a geometric model but on tables of coordinates designed to make the world 'look right'.
It provides a good balance of shape and area distortion across most of the map, though extreme polar regions are flattened.
2. The Winkel Tripel Projection:
Developed in 1921 and adopted by the National Geographic Society in 1998 as its standard for world maps.
The name "Tripel" means 'triple' in German, referring to van Winkel's goal of minimizing three types of distortion: area, direction, and distance.
Research has shown it to have a very low overall distortion measure compared to many other world projections, making it a popular choice for general world maps today.
Given the vast array of projections and their inherent compromises, choosing the appropriate projection for a map is a critical step in cartography.
The choice depends entirely on the map's purpose, the geographic area being mapped, and the specific message or information the map intends to convey.
Here are the key factors cartographers consider when selecting a projection:
1. What is the primary purpose of the map?
Is it for navigation (needs conformality)? Comparing land sizes (needs equivalence)? Showing distances from a point (needs equidistance from that point)? Illustrating global patterns (perhaps a compromise)? Or perhaps showing shortest paths (needs azimuthal property from the center)?
2. What geographic area is being mapped?
Is it the entire world? A continent? A country? A state or province? A small city?
Projections that work well for small areas (where distortion is minimal regardless of projection type) might be terrible for world maps, and vice versa.
Conical projections are often good for mid-latitude regions with east-west extent, while cylindrical or certain azimuthal projections might be better for equatorial or polar regions, respectively.
3. Which specific geographic properties are most important to preserve?
Based on the purpose, prioritize which type of distortion is least acceptable.
If visual comparison of area is paramount, equal-area is non-negotiable.
If accurate angles for local surveys are needed, conformality is key.
4. What is the acceptable level and distribution of distortion?
Even within projections of the same type, different parameters (like standard parallels) can shift where distortions are minimized and maximized.
For instance, a conic projection can be optimized for a specific range of latitudes.
5. What are the aesthetic considerations?
Especially for general reference maps, how the world "looks" on the page matters.
Rectangular maps, oval maps, or circular maps each have different visual impacts.
Making an informed choice about map projection ensures that the map effectively communicates the intended information and avoids misleading the user through unintended distortions.
While we've discussed projections primarily in the context of static paper maps, they are equally, if not more, crucial in the world of digital mapping, Geographic Information Systems (GIS), and online web maps.
Digital data representing the Earth's surface is always stored or processed using a coordinate system tied to a specific map projection or a geographic coordinate system (like latitude and longitude on a sphere).
When you view a map online (like Google Maps, OpenStreetMap, etc.), you are almost certainly looking at data displayed using a map projection.
The most common projection for interactive web maps is "Web Mercator" (also known as Google Web Mercator or WGS 84/Pseudo-Mercator).
This is a slight variation of the traditional Mercator projection, optimized for display tiles, and it retains the conformal property (good for local navigation and familiar shapes) but exhibits the same severe area distortion at higher latitudes.
Users of GIS software constantly work with projections, often needing to re-project data from one coordinate system to another to ensure different datasets align correctly or to perform analyses that require specific properties (like accurate area calculations).
Understanding projection principles is therefore not just academic; it's a practical skill for anyone working with spatial data in the digital age.
The journey to understand map projections reveals a fundamental truth about cartography: every flat map is a carefully constructed compromise.
The inherent impossibility of perfectly translating a 3D spherical surface into a 2D plane means that distortion is not an error to be eliminated, but a reality to be managed and understood.
Different map projections exist because different uses of maps demand different priorities for preserving geographic properties.
Some maps prioritize accurate area for fair comparison, others prioritize true shape for navigation, some focus on distance or direction from a key point, and many seek to balance these conflicting goals for general reference.
By recognizing the specific distortions present in any given map projection, you gain a deeper, more authoritative understanding of the information being presented.
You can look at a map not just as a picture of the world, but as a tool designed with a specific purpose and specific limitations in mind.
So, the next time you encounter a map, take a moment to consider its projection and the fascinating choices made by the cartographer.
Appreciating these "quirks" allows you to use maps more effectively, interpret geographical information more accurately, and marvel at the ingenious ways cartographers have attempted to represent our complex world on a flat surface.
Every map tells a story, not just about the places it depicts, but also about the mathematical challenge and the human decisions behind its creation.
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