3. Scale and Projections

Laura Matson; Steven Manson; and Melinda Kernik

Scale and projections are two fundamental features of maps that usually do not get the attention they deserve. Scale refers to how map units relate to real-world units. Projections deal with the methods and challenges around turning a three-dimensional (and sort of lumpy) earth into a two-dimensional map.

This chapter will introduce you to:

  • Scale and ways of telling the map user what the map is measuring on the ground
  • Projection mechanics, types of projections, and their characteristics

By the end of this chapter, you should be able to read map scales and identify common projections along with their basic features and uses.

3.1 Scale

The world is vast. The Earth’s surface has an area of over 500 million km2. Any picture of the earth that you can easily carry can only show general outlines of continents and countries. When we visually represent a region of the world on a map, we must reduce its size to fit within the boundaries of the map. Map scale measures how much the features of the world are reduced to fit on a map; or more precisely, map scale shows the proportion of a given distance on a map to the corresponding distance on the ground in the real world.

Map scale is represented by a representative fraction, graphic scale, or verbal description.

The image shows an example of a map scale which has three rows of information. The box is grey with a dark grey rounded border and black text. On the top row, there is a ‘Ratio (Fraction) scale’ which is shown to be 1:62,500. On the middle row, it shows the ‘Graphic scale’ which is shown to be five subdivisions between each mile. On the bottom row, it shows ‘Verbal scale’ which indicates that ‘1 inch equals 1 mile.’
Map scales. A map can have a representative fraction, graphic scale, or verbal description that all mean the same thing. [1]

Representative fraction. The most commonly used measure of map scale is the representative fraction (RF), where the map scale is shown as a ratio. With the numerator always set to 1, the denominator represents how much greater the distance is in the world. The figure below shows a topographic map with an RF of 1:24,000, which means that one unit on the map represents 24,000 units on the ground. The representative fraction is accurate regardless of which units are used; the RF can be measured as 1 centimeter to 24,000 centimeters, one inch to 24,000 inches, or any other unit.

The image shows the scale for El Dorado Springs. On the top row of the scale, there is text that reads ‘Scale 1:24000.’ Beneath that, a bar shows 1 mile to take up just under a half of the image and it is subdivided 10 times. Beneath that it shows a slightly smaller bar with the scale in feet. Beneath that was a smaller bar with the scale in kilometers. Beneath that there is text that reads: ‘CONTOUR INTERVAL 40 feet’, and beneath that: ‘NATIONAL GEODETIC VERTICAL DATUM OF 1929.’ Further below, there are three rows of text which reads – top line: THIS MAP COMPLIES WITH NATIONAL MAP ACCURACY STANDARDS’; middle line: FOR SALE BY U.S. GEOLOGICAL SURVEY, P.O. BOX 25286, DENVER, COLORADO 80225; A FOLDER DESCRIBING TOPOGRAPHIC MAPS AND SYMBOLS IS AVAILABLE ON REQUEST’. Above this information, there is a topographic map of the area in light green and dark green, with notable sites listed including ‘Flagstaff Mtn,’ Ute Springs,’ and ‘Lost Gulch.’
Representative fraction. Representative fraction and scale bars from a United States Geological Survey (USGS) topographic map. This topographic map has an RF of 1:24,000, which means that one unit on the map represents 24,000 units on the ground. [2]

Graphic scale. Scale bars are graphical representations of distance on a map. The figure has scale bars for 1 mile, 7000 feet, and 1 kilometer. One important advantage of graphic scales is that they remain true when maps are shrunk or magnified.

Verbal description. Some maps, especially older ones, use a verbal description of scale. For example, it is common to see “one inch represents one kilometer” or something similar written on a map to give map users an idea of the scale of the map.

Mapmakers use the term scale to describe maps as being small-scale or large-scale. This description of map scale as large or small can seem counterintuitive at first. A 3-meter by 5-meter map of the United States has a small map scale, while a UMN campus map of the same size is large-scale. Scale descriptions using the RF provide one way of considering scale since 1:1000 is larger than 1:1,000,000. Put differently, if we were to change the scale of the map with an RF of 1:100,000 so that a section of road was reduced from one unit to, say, 0.1 units in length, we would have created a smaller-scale map whose representative fraction is 1:1,000,000.

When we talk about large- and small-scale maps and geographic data, then, we are talking about the relative sizes and levels of detail of the features represented in the data. In general, the larger the map scale, the more detail that is shown.

3.2 Extent vs. Resolution

The extent of a map describes the area visible on the map, while resolution describes the smallest unit that is mapped. You can think of the extent as describing the region to which the map is zoomed. The extent of the map below is national as it encompasses the contiguous United States, while the resolution is the state because states are the finest level of spatial detail that we can see.

A choropleth map of the United States. Each state is shaded in varying light-to-dark orange tones, indicating differences in a mapped variable. State boundaries are clearly defined, but no finer geographic details (such as counties or cities) are shown. The map highlights that the spatial extent covers the entire country, while the level of detail (resolution) is limited to individual states.
Map resolution and extent. This map shows a national extent and a state resolution. The extent of the map is national, while the resolution is at the state level because they are the finest level of spatial detail that we can see. [3]

We often choose mapping resolutions intentionally to make the map easier to understand. For example, if we tried to display a map with a national extent at the resolution of census blocks, the level of detail would be so fine, and the boundaries would be so small that it would be difficult to understand anything about the map. Balancing extent and resolution is often one of the most important and difficult decisions a cartographer must make. The figure below offers two more examples of the difference between extent and resolution. Both maps share the same extent but have different resolutions.

Two choropleth maps of Washington State in the Pacific Northwest are shown for comparison. The top map displays data at the county level, with larger, clearly defined areas shaded in varying orange tones and labeled cities such as Seattle, Olympia, and Spokane. The bottom map shows the same region at a finer spatial resolution using census tracts, with many smaller, more detailed areas shaded in similar orange tones. Both maps cover a similar geographic extent, but the bottom map reveals more localized variation due to its higher level of detail.
More map extent and resolution. Maps showing the extent of the Pacific Northwest. The top image has a spatial resolution of the county, and the bottom has a spatial resolution of census tracts. [4]

3.3 Coordinates & Projections

Locations on the earth’s surface are measured in terms of coordinates, a set of two or more numbers that specifies a location in relation to some reference system. The simplest system of this kind is a Cartesian coordinate system, named for the 17th-century mathematician and philosopher René Descartes. A Cartesian coordinate system, like the one below, is simply a grid formed by putting together two measurement scales, one horizontal (x) and one vertical (y). The point at which both x and y equal zero is called the origin of the coordinate system. In the figure, the origin (0,0) is located at the center of the grid (the intersection of the two bold lines). All other positions are specified relative to the origin, as seen with the points at (3, 2) and (-4, -1)

A diagram of a 2D Cartesian coordinate system overlaid on a grid. A vertical black line represents the y-axis, with an orange arrow pointing up labeled "y" and an orange arrow pointing down labeled "-y." A horizontal black line represents the x-axis, with a blue arrow pointing right labeled "x" and a blue arrow pointing left labeled "-x." Two blue circular points are plotted on the grid: one in the upper-right quadrant at the coordinates (3, 2) and one in the lower-left quadrant at the coordinates (-4, -1).
Coordinate system. Locations on the Earth’s surface are measured in terms of coordinates, a set of two or more numbers that specifies a location in relation to some reference system. [5]

The geographic coordinate system is designed specifically to define positions on the Earth’s roughly spherical surface. Instead of the two linear measurement scales x and y, as with a Cartesian grid, the geographic coordinate system uses an east-west scale, called longitude, that ranges from +180° to -180°. Because the Earth is round, +180° (or 180° E) and -180° (or 180° W) are the same grid line, termed the International Date Line. Opposite the International Date Line is the prime meridian, the line of longitude defined as 0°. The north-south scale, called latitude, ranges from +90° (or 90° N) at the North pole to -90° (or 90° S) at the South pole. In simple terms, longitude specifies positions east and west, and latitude specifies positions north and south. At higher latitudes, the length of parallels decreases to zero at 90° North and South. Lines of longitude are not parallel but converge toward the poles. Thus, while a degree of longitude at the equator is equal to a distance of about 111 kilometers, that distance decreases to zero at the poles.

A diagram showing how latitude and longitude wrap around the Earth. The image is divided into two columns: Left Column (Latitude): The top globe shows horizontal orange lines circling the Earth parallel to the equator. Below it, a 2D circular diagram of the Earth labels these lines by degree: 0 degrees at the equator, moving up to 90 degrees N and down to -90 degrees S. Right Column (Longitude): The top globe shows vertical orange lines running from the North Pole to the South Pole. Below it, a top-down polar view shows these lines radiating from the center like spokes on a wheel, labeled from 0 degrees up to 180 degrees and -180 degrees, with 90 degrees E and -90 degrees W marking the sides.
Longitude and latitude. The graticule is based on an east-west scale called longitude and a north-south scale called latitude. [6]

The graticule specifies positions on the globe with latitude and longitude coordinates. The graticule refers to longitude and latitude on a three-dimensional globe. When we use longitude and latitude on a two-dimensional map, we refer to these as geographic coordinates. Maps can have an enormous array of different coordinate systems depending on who developed and used them.

Projection is the term for turning a three-dimensional globe into a two-dimensional map. As noted above, the graticule on a globe is helpful, but how do we go from three-dimensional graticule to two-dimensional geographic coordinates, as per the figure below? We will discuss the process of how objects on a 3-dimensional surface (the earth) come to be represented on a flat piece of paper or computer screen. Our emphasis will be on the properties that different projections distort or maintain – area, shape, and distance.

A diagram illustrating the transition of coordinates from a sphere to a flat plane. On the left, a sphere labeled "Graticule" shows curved lines of latitude and longitude. An orange curved arrow along the side is labeled "Latitude," and a horizontal blue arrow across the center is labeled "Longitude." In the center, a large blue arrow points to the right, indicating a transformation. On the right is a flat rectangular grid labeled "Projected as geographic coordinates." The curved lines have been straightened into a 2D Cartesian-style grid. Vertical orange arrows indicate "Latitude" (y-axis), and horizontal blue arrows indicate "Longitude" (x-axis).
Graticule projected. The longitude and latitude of the graticule become two-dimensional geographic coordinates through projection. [7]

Projection is the process of making a two-dimensional map from a three-dimensional globe. We can think of the Earth as a sphere. In reality, it is more of an ellipsoid with a few bulges, but it is fine to think of it as a sphere. To get a sense of how difficult this process can be, imagine peeling the skin from an orange and trying to lay the skin flat.

A conceptual image illustrating the difficulty of map projection. It shows a single, continuous orange peel laid out horizontally against a white background. A map of the world’s continents is printed across the textured, bumpy surface of the peel. To lie relatively flat, the peel has several deep, vertical "V" shaped tears (interruptions), particularly between the major landmasses like the Americas, Africa, and Asia, demonstrating how a 3D sphere must be distorted or broken to be represented on a 2D surface.
Flattened orange peel. You can imagine the difficulty of moving from a 3d to 2d surface by considering how difficult it is to peel the rind from an orange and try to lay the skin flat. [8]

As you peel and flatten the skin, you will encounter several problems:

  • Shearing – stretching the skin in one or more directions
  • Tearing – causing the skin to separate
  • Compressing – forcing the skin to bunch up and condense

Cartographers face the same three issues when they try to transform the three-dimensional globe into a two-dimensional map. If you had a globe made of paper, you could carefully try to ‘peel’ it into a flat piece of paper, but you would have a big mess on your hands. Instead, cartographers use projections to create usable two-dimensional maps.

A technical diagram showing how a 3D globe is distorted when converted to a 2D map. A wireframe globe is shown on the left, with three arrows pointing to specific examples of distortion on the right. Tearing: An arrow points from the top of the globe to a diagram showing two separate, jagged sections of the map that have been split apart (interrupted) to maintain shape. Compression: An arrow points from the middle of the globe to a vertical grid where a square has been squashed or narrowed, showing how landmasses can be squeezed. Shearing: An arrow points from the bottom of the globe to a warped grid where the lines intersect at slanted angles rather than 90-degree corners, showing the stretching and skewing of shapes.
Shearing, tearing, and compression. Cartographers face the three issues of shearing, tearing, and compression on a globe when they try to transform the three-dimensional globe into a two-dimensional map. [9]

3.4 Projection Mechanics

The term “map projection” refers to both the process and product of transforming spatial coordinates on a three-dimensional sphere to a two-dimensional plane. In terms of actual mechanics, most projections use mathematical functions that take as inputs locations on the sphere and translate them into locations on a two-dimensional surface.

It is helpful to think about projections in physical terms. If you had a clear globe the size of a beach ball and placed a light inside this globe, it would cast shadows onto a surrounding surface. If this surface were a piece of paper that you wrapped around the globe, you could carefully trace these shadows onto the paper, then flatten out this piece of paper and have your projection!

A three-row diagram (labeled a, b, and c) showing how a 3D globe is projected onto different 2D surfaces using a light bulb analogy. In each row, a light bulb inside a wireframe globe casts a grid onto a surrounding paper shape. Row A (Cylindrical): A cylinder is wrapped around the globe. Scissors cut the cylinder vertically, and it unrolls into a flat, rectangular map grid. Row B (Conic): A cone sits on top of the globe like a hat. Scissors cut the cone from the base to the tip, and it unfolds into a flat, fan-shaped map grid. Row C (Planar/Azimuthal): A flat circular plane touches the top of the globe at a single point. The grid is projected directly onto the circle, resulting in a flat, circular map with lines radiating from the center.
Thinking of projections in physical terms. You can conceptualize projection as working with a clear globe, a light bulb, and tracing paper. If you had a clear globe the size of a beach ball and placed a light inside this globe, it would cast shadows onto a surrounding surface. This surface can be a (a) cylinder, (b) cone, or (c) plane. [10]

Most projections transform part of the globe to one of three “developable” surfaces, so called because they are flat or can be made flat: plane, cone, and cylinder. The resultant projections are called planar, conical, and cylindrical. We use developable surfaces because they eliminate tearing, although they will produce shearing and compression. Of these three problems, tearing is seen as the worst because you would be making maps with all sorts of holes in them! As we see below, however, there are times when you can create maps with tearing, and they are quite useful.

The place where the developable surface touches the globe is known as the tangent point or tangent line. Maps will most accurately represent objects on the globe at these tangent points or lines, with distortion increasing as you move farther away due to shearing and compression. It is for this reason that cylinders are often used for areas near the equator, cones are used to map the mid-latitudes, and planes are used for polar regions.

A technical diagram illustrating tangent points and lines on three types of map projections, labeled a, b, and c. Projection (a) Cylindrical: A cylinder is wrapped around the globe, touching it along a horizontal red line at the equator. A flat, rectangular map to the left shows this same red line as a straight horizontal axis. Projection (b) Conic: A cone sits over the globe, touching it along a curved red line in the Northern Hemisphere. A flat, fan-shaped map to the left shows this tangent line as a circular arc. Projection (c) Planar (Azimuthal): A flat square plane sits on top of the globe, touching it at a single red dot at the North Pole. Below, a circular map shows the red dot at the center, where the lines of longitude meet.
Tangency. Red lines or dots mark the tangent line or point, respectively. The flat surface touches the globe, and it is the point on the projected map that has the least distortion. The place where the developable surface touches the globe is known as the tangent point or tangent line. These surfaces can be a (a) cylinder, (b) cone, or (c) plane. [11]

For beginning mapmakers, understanding the exact mechanics of projections doesn’t matter as much as knowing which map properties are maintained or lost with the choice of projection – the topic of the next section.

Projections must distort features on the surface of the globe during the process of making them flat because projection involves shearing, tearing, and compression. Since no projection can preserve all properties, it is up to the mapmaker to know which properties are most important for their purpose and to choose an appropriate projection. The properties we will focus on are shape, area, and distance.

Note that distortion is not necessarily tied to the type of developable surface but rather to the way the transformation is done with that surface. It is possible to preserve any one of the three properties using any of the developable surfaces. One way of looking at the problem is with distortion ellipses. These help us to visualize what type of distortion a map projection has caused, how much distortion has occurred, and where it has occurred. The ellipses show how imaginary circles on the globe are deformed as a result of a particular projection. If no distortion had occurred in projecting a map, all of the ellipses would be the same size and circular in shape.

3.4.1 Conformal

Conformal projections preserve shape and angle but strongly distort area in the process. For example, with the Mercator projection, the shapes of coastlines are accurate on all parts of the map, but countries near the poles appear much larger relative to countries near the equator than they are. For example, Greenland is only 7 percent the land area of Africa, but it appears to be just as large!

A world map using the Mercator projection, shown as a large rectangle with a blue grid of straight, perpendicular lines for latitude and longitude. The map uses satellite imagery for the landmasses and blue for the oceans. Because this projection preserves angles but distorts size, landmasses near the poles appear significantly larger than they are in reality: Greenland appears roughly the same size as Africa, and Antarctica is shown as a massive, continuous white landmass stretching across the entire bottom edge of the map.
Mercator projection. The Mercator projection is conformal because it preserves shape and angle but strongly distorts area. [12]

Conformal projections should be used if the main purpose of the map involves measuring angles or representing the shapes of features. They are very useful for navigation, topography (elevation), and weather maps.

A black-and-white reproduction of Gerardus Mercator’s 1569 world map, titled "Nova et Aucta Orbis Terrae Descriptio ad Usum Navigantium Emendata." The map features a dense, detailed engraving of the continents as they were understood in the 16th century. The oceans are crisscrossed with numerous rhumb lines (straight lines of constant bearing) used for navigation. Elaborate decorative elements surround the map, including ornate cartouches filled with Latin text, illustrations of ships, sea monsters, and a secondary circular polar map in the bottom-left corner. The overall layout reflects the same cylindrical projection that preserves straight lines for sailors but results in significant landmass distortion near the poles.
Mercator projection. One of the first maps of the world developed was by Mercator (Carta do Mundo de Mercator, 1569). [13]

A conformal projection will have distortion ellipses that vary substantially in size, but are all the same circular shape. The consistent shapes indicate that conformal projections (like this Mercator projection of the world) preserve shapes and angles. This useful property accounts for the fact that conformal projections are almost always used as the basis for large-scale surveying and mapping.

A world map using the Mercator projection with a grid of red circles (indicatrices) overlaid to show area distortion. Near the equator, the red circles are small and uniform, indicating minimal distortion of size. As the circles move toward the North and South Poles, they grow significantly larger in diameter while remaining perfectly circular. This visually shows that while the map preserves shapes and angles (conformality), it inflates the relative size of landmasses like Greenland, Northern Canada, and Antarctica compared to regions near the equator.
Mercator distortion. The Mercator projection is conformal because it preserves shape and angle but strongly distorts area. [14]

3.4.2 Equal Area

On equal-area projections, the size of any area on the map is in true proportion to its size on the earth. In other words, countries’ shapes may appear to be squished or stretched compared to what they look like on a globe, but their land area will be accurate relative to other land masses. For example, in the Gall-Peters projection, the shape of Greenland is significantly altered, but the size of its area is correct in comparison to Africa. This type of projection is important for quantitative thematic data, especially in mapping density (an attribute over an area). For example, it would be useful in comparing the density of Syrian refugees in the Middle East or the amount of cropland in production.

A world map using the Gall-Peters projection, which is an equal-area cylindrical projection. The landmasses and oceans are shown via satellite imagery overlaid with a rectangular blue grid. Unlike the Mercator projection, this map shows the true relative sizes of continents: Africa and South America appear much larger and vertically elongated, while Greenland and Europe appear significantly smaller. To maintain these accurate area proportions on a flat map, the shapes of the continents are vertically stretched near the equator and horizontally compressed near the poles, resulting in a "distorted" or "stretched" visual appearance.
Gall-Peters projection. The Gall-Peters projection is equal area. Note how the shape of Greenland is significantly altered, but the size of its area is correct in comparison to other regions such as Africa. [15]

As we can see with an equal-area projection, however, the ellipses maintain the correct proportions in the sizes of areas on the globe, but their shapes are distorted. Equal-area projections are preferred for small-scale thematic mapping, especially when map users are expected to compare the sizes of area features like countries and continents.

A world map using the Gall-Peters projection with an overlay of orange ovals (Tissot's Indicatrices) to demonstrate shape distortion versus area consistency. Unlike the Mercator projection where circles grow in size, these ovals all cover the exact same amount of surface area regardless of their location. Near the equator, the ovals are vertically elongated (stretched tall), while near the North and South Poles, they are horizontally elongated (stretched wide and flat). This illustrates that while the map preserves the correct proportional size of landmasses, it does so by significantly distorting their shapes.
Gall-Peters distortion. The Gall-Peters projection is equal area. Note how the shape of Greenland is significantly altered, but the size of its area is correct in comparison to other regions such as Africa.  [16]

3.4.3 Equidistant

Equidistant projections, as the name suggests, preserve distance. This is a bit misleading because no projection can maintain relative distance between all places on the map. Equidistant maps are able, however, to preserve distances along a few specified lines. For example, on the Azimuthal Equidistant projection, all points are the proportionally correct distance and direction from the center point. This type of projection would be useful for visualizing airplane flight paths from one city to several other cities or in mapping an earthquake epicenter. Azimuthal projections preserve distance at the cost of distorting shape and area to some extent.  The flag of the United Nations contains an example of a polar azimuthal equidistant projection.

A circular world map using the Azimuthal Equidistant projection, centered on the North Pole. In this view, the Arctic is at the very center, with continents like North America, Eurasia, and Africa radiating outward. Longitude lines appear as straight spokes from the center, while latitude lines form concentric circles. Antarctica is shown as a white ring surrounding the outer edge of the map. To the bottom right, the official United Nations emblem is shown, which uses this exact map projection framed by two golden olive branches.
Azimuthal Equidistant projection. In this equidistant projection, all points are the proportionally correct distance and direction from the center point. This projection is used on the map of the United Nations. [17]

3.4.4 Compromise, Interrupted, and Artistic Projections

Some projections, including the Robinson projection, strike a balance between the different map properties. In other words, instead of preserving shape, area, or distance, they try to avoid extreme distortion of any of these properties. This type of projection would be useful for a general-purpose world map.

A world map using the Robinson projection, shown as a satellite-view image with a blue grid of latitude and longitude lines. The map has a distinct shape with a flat top and bottom and curved sides, creating a rounded, pill-like appearance. Unlike the rectangular Mercator or Gall-Peters projections, the lines of longitude (meridians) curve gently toward the poles, while the lines of latitude (parallels) remain straight and horizontal. This creates a more natural-looking representation of the continents, where the sizes and shapes of landmasses like Greenland and Africa are neither perfectly accurate nor extremely distorted, but instead appear "visually correct" to the human eye.
Robinson Projection. Some projections, including the Robinson projection, strike a balance between the different map properties. In other words, they do not preserve shape, area, or distance but instead try to avoid extreme distortion. [18]

Compromise projections preserve no one property but instead seek a compromise that minimizes distortion of all kinds, as with the Robinson projection, which is often used for small-scale thematic maps of the world.

A world map using a compromise projection (specifically the Robinson projection) with an overlay of orange ovals (indicatrices). The map has a rounded, pill-like shape. The ovals demonstrate that this projection distorts both shape and area, but in a controlled way. Near the equator, the ovals are nearly circular and uniform in size. As they move toward the poles, they become slightly larger and tilt or flatten into ellipses, but they do not grow as excessively as in the Mercator nor flatten as severely as in the Gall-Peters. This visualizes a middle ground where no single property is perfect, but extreme distortion is avoided across the entire map.
Compromise distortion. Note that some maps may not preserve either shape or area but do a pretty good job at both. [19]

Other projections deal with the challenge of making the 3D globe flat by tearing the Earth in strategic places. Interrupted projections, such as the interrupted Goode Homolosine projection, represent the earth in lobes, reducing the amount of shape and area distortion near the poles. The projection was developed in 1923 by John Paul Goode to provide an alternative to the Mercator projection for portraying global areal relationships.

A world map using the Goode Homolosine projection, shown in a satellite-view style with a blue grid. The map is "interrupted," meaning it is not a continuous rectangle or circle. Instead, it is divided into five distinct, vertically connected sections or "lobes" that radiate down from the continuous North Pole. Deep "V" shaped gaps (interruptions) separate these lobes, primarily over the Atlantic, Pacific, and Indian Oceans. This allows the landmasses, such as North America, Africa, and Eurasia, to maintain accurate relative sizes and shapes, avoiding the severe elongation seen near the equator in the Gall-Peters projection.
Goode homolosine projection of the world. This equal-area projection is interrupted in the sense that it uses lobes or sections. [20]

The Interrupted Goode Homolosine preserves area (so it is equal-area or equivalent) but does not preserve shape (it is not conformal).

A technical diagram of the interrupted Goode Homolosine projection, shown as a white wireframe grid with a green circular overlay. The map is divided into four rounded lobes at the bottom and two at the top, separated by deep white gaps (interruptions). A grid of small green circles (indicatrices) is overlaid across the entire map. These circles remain almost identical in size across the various sections, demonstrating the "equal-area" property. While some circles near the outer edges of the lobes are slightly skewed into ovals, the interruptions allow the map to maintain much more consistent shapes and sizes than a continuous cylindrical projection would.
Interrupted distortion. This equal area projection preserves area but distorts shape, but not as much as it would if it were not interrupted. [21]

Many projections are aesthetically pleasing, but not intended for navigation between places or to visualize data. Examples of these artistic projections include the heart-shaped Stabius-Werner projection.

A side-by-side comparison of the heart-shaped Stabius-Werner projection. On the left: A modern version of the projection using satellite imagery. The world is shaped like a heart (cordiform), with the North Pole at the top center "dip" and the South Pole at the bottom point. The continents are wrapped to fit this shape, with the Americas on the left curve and Asia/Australia on the right. On the right: A historical 16th-century version of the same projection. This antique map is highly decorative, featuring a yellowish parchment texture, hand-drawn landmasses, and an ornate wooden-style frame with classical columns. Latin text is inscribed in several rectangular boxes (cartouches) at the bottom and sides of the heart.

Artistic projections. Many projections are interesting and beautiful, like this Stabius-Werner Projection, but are not intended for navigation between places or for visualizing data. [22]

3.5 Conclusion

In this chapter, we have explored the concepts of scale, resolution, and projection. There are hundreds of projections, each of which distorts the world in a slightly different way. Keep in mind that all maps have a scale, and there are a few important ways to indicate this scale. All maps also use a projection that can be formed from a developable surface and can preserve one or two properties at most.

Resources

References

Parts of section 3.1 are adapted from Campbell and Shin (2011). Essentials of Geographic Information Systems.

Parts of section 3.3 are adapted from DiBiase (1998). The Nature of Geographic Information: An Open Geospatial Textbook.

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  7. CC BY-NC-ND 3.0. Adapted from Dibiase et al. (2012) Mapping our Changing World. https://www.e-education.psu.edu/geog160/node/1914. Geography Department, The Pennsylvania State University. ↵
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  18. CC BY-SA 3.0. Eric Gaba https://commons.wikimedia.org/w/index.php?curid=16115337 ↵
  19. GFDL. Eric Gab Data: U.S. NGDC World Coast Line (public domain), GFDL, https://commons.wikimedia.org/w/index.php?curid=4256 ↵
  20. CC BY-SA 3.0. Daniel R. Strebe. https://commons.wikimedia.org/w/index.php?curid=16115269 ↵
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