Topographic Map of the Earth National Geophysical Data Center National Oceanic and Atmospheric Administration

       Many, if not most, types of mapped information can be clearly shown in two dimensions: Political boundaries, population density, or annual rainfall work just fine as flat areas of color. But a map that shows hills and valleys can be extraordinarily useful to a cyclist in San Francisco or a hiker in the Hindu Kush (though not, perhaps, to a skater in northern Indiana).

Early Escapes from Flatland Above: Canyon walls and cliffs are shown by crosshatching on this 1904 map of the Grand Canyon of the Colorado. The mapmaker didn't attempt to document elevations. Below: the Southern Appalachians appear as drawings of idealized peaks in this detail drawn from a 1767 map by Emanuel Bowen. This kind of mapping shows where the mountains are, but provides only scant assistance for the traveler. Both maps are from the collection of the Library of Congress, American Memory Project. Click on either to go to the original map. [ed.]

       Topographic maps address the problem of displaying three dimensions in two. (The word derives from the Greek “topos,” “place,” and “graphein,” “to draw.”) A topographical map shows the physical contours of a landscape, including mountains, cliffs, gulleys, and plains, along with features such as buildings, roads, ponds, and other landmarks.

       Early mapmakers depicted hills and valleys with shading or hatching, or drew mountains as little saw-toothed profiles. Such attempts at topographical information were of necessity crude, in part because there was no standard to represent the data but also because the exact shape of the features had not been measured. By the mid-19th century, improved surveying provided more accurate information about the landscape; contour lines became the convention for writing this information.

       A contour line is simply a line drawn through a series of points that have the same elevation. By drawing contour lines at regular intervals, such as every 5 meters above sea level, a mapmaker can offer a reasonably good representation of the lay of the land. On a topographical map a hill looks like a bulls-eye of concentric circles, indicating a gentle slope, while a cliff’s closely massed parallel lines show a steep one. Using the clues provided by contour lines, a keen map reader can visualize the terrain and pick out a level route or avoid dangerous drop-offs.

       Another form of topographical map breaks the two-dimensional barrier and extends into the third dimension. Such maps show the land's physical shape in relief, with bumps for mountains and flat areas for seas. Though more easily understood than two-dimensional maps, relief maps must be made of rigid and unwieldy materials, which limits their portability. Still, a relief map of, say, South America dramatically shows the relationship between the Andes and the Amazon basin.

       In such three-dimensional maps the vertical axis -- the height of the features -- must be greatly exaggerated to show any relief. Though mountains seem rugged to humans, they don't matter much on a global scale: Mount Everest, the tallest peak, raises a bump smaller than one-seventh of one percent of the earth’s radius. In other words, if you could hold the world in the palm of your hand, it would feel smoother than a billiard ball.