Cartography is the science and art of creating maps, which involves representing the three-dimensional Earth on a two-dimensional surface. The Earth is an irregular sphere, or geoid. Converting this curved surface onto a flat plane, such as a screen or paper, creates a fundamental dilemma in map-making. The unavoidable result is distortion, meaning no flat map can perfectly represent all geographic properties simultaneously. This distortion is an inherent consequence of geometric laws, not a cartographic mistake.
The Geometric Impossibility of Flat Maps
Map distortion stems from the geometric difference between a sphere and a plane. A sphere has positive intrinsic curvature, while a flat plane has zero intrinsic curvature. The inability to perfectly flatten a sphere is described by Gauss’s Theorema Egregium, or “Remarkable Theorem.” This theorem states that a surface’s curvature cannot be changed by bending it without stretching or tearing.
This principle means that an isometric mapping—a transformation that preserves distances between every pair of points—is impossible when converting a curved surface to a flat one. Any attempt to transform the Earth’s surface to a plane must involve stretching, compressing, or shearing the information. Cartographers must therefore choose which geographic properties to sacrifice during the conversion process.
Defining the Four Types of Map Distortion
When the Earth’s curved surface is transformed into a flat map, four main characteristics are subject to alteration: Area, Shape, Distance, and Direction. While a specific map projection may minimize the distortion of one or two of these properties, it cannot preserve all four across the entire map.
Area distortion means the relative sizes of landmasses are incorrect, causing some continents to appear disproportionately large or small. Shape distortion, also known as angular distortion, affects the outline of geographic features, making them appear stretched or squashed. Distance distortion occurs when the measured linear separation between two points does not accurately reflect the true distance on the Earth’s surface. Finally, direction distortion means that the angles or compass bearings are not accurately represented.
The Role of Map Projections and Cartographic Trade-offs
Since perfect representation is unattainable, cartographers rely on mathematical formulas called map projections to systematically transfer coordinates from the sphere to the plane. A projection is a methodology for managing distortion, prioritizing certain properties based on the map’s intended purpose.
Two primary goals define the trade-off in projection selection: conformality and equivalence. A conformal projection preserves the correct shape and angles of small areas, which is highly useful for navigation. This accuracy comes at the cost of severe area distortion.
Conversely, an equal-area, or equivalent, projection maintains the correct relative sizes of all landmasses, making it beneficial for thematic mapping. Equivalence severely distorts the shapes of continents, particularly at high latitudes. Cartographers may also select a compromise projection, such as the Winkel Tripel, which attempts to strike a visual balance by minimizing total distortion.
Examples of Distortion in Well-Known Maps
The practical effects of these cartographic trade-offs are most evident when comparing two well-known world maps. The Mercator Projection, developed in 1569, is a classic conformal projection designed to aid marine navigation. It allows sailors to plot a course of constant compass bearing as a straight line.
The Mercator projection achieves shape and direction accuracy at the expense of area, which is highly distorted near the poles. For example, Greenland appears roughly the same size as Africa, though Africa is about 14 times larger in total area. High-latitude countries like Canada and Russia also appear vastly oversized compared to equatorial regions.
In contrast, the Gall-Peters Projection is an equal-area map promoted to correct the Mercator’s area distortions. This projection accurately depicts the true relative sizes of the continents, restoring Africa and South America to their correct proportions. This equivalence comes at the expense of shape, causing landmasses near the equator to appear vertically stretched.