"Contour" and "Contour map" redirect here. For the NASA space probe, see
CONTOUR. For the automobile, see
Ford Contour. For most everyday use of the term is in cartography. A contour map (topographic map) uses contour lines (often just called a "contour") to join points of equal elevation (height) and thus show valleys and hills, and the steepness of slopes.More generally, a contour line (also
level set, isopleth, isoline, isogram or isarithm) for a function of two variables is a
curve connecting points where the function has a same particular value. The prefix iso-, from the
Greek prefix ισος ("equal"), is used from descriptive names for map lines that join points of equal value. The
gradient of the function is always perpendicular to the contour lines. When the lines are close together the length of the gradient is large: the variation is steep. If adjacent contour lines are of the same line width, the direction of the gradient cannot be determined from the contour lines alone. However if contour lines rotate through three or more widths, or if the lines are numerically labelled, then the direction of the gradient can also be determined from the contour lines.
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