# Why are Contour Lines used on Maps?

Contour lines are used
when maps are designed to show the physical nature of the land. They do this by
linking all points which are the same height above sea level. The width between
the contour lines indicates the steepness of gradients or slopes in the area.
The closer the lines are together, the steeper is the slope.

On physical maps giving the height of mountains, rivers, lakes and principal
towns all areas between certain heights are generally shown in the same color.
This is known as layer coloring. Other methods for indicating heights include
relief maps moulded in plastic to the physical feature raised as on a model.
Spot heights may be shown, but these merely give the heights above sea level of
certain points of the map and it does not follow that the ground rises evenly
from one point to another.

Very old maps have mountains drawn on them. Later ones have lines called
hachures radiating from a central point, with longer lines to show gentler
slopes. Another system is to show the form of land by hill shading. But none of
these methods is so effective as the use of contour lines. More generally, a
contour line for a function of two variables is a curve connecting points where
the function has the same particular value.

The gradient of the function is always perpendicular to the contour lines. When the lines are close together the magnitude of the gradient is large: the variation is steep. A level set is a generalization of a contour line for functions of any number of variables.

Contour lines are curved, straight or a mixture of both lines on a map describing the intersection of a real or hypothetical surface with one or more horizontal planes. The configuration of these contours allows map readers to infer relative gradient of a parameter and estimate that parameter at specific places.

Contour lines may be either traced on a visible three-dimensional model of the surface, as when a photogrammetrist viewing a stereo-model plots elevation contours, or interpolated from estimated surface elevations, as when a computer program threads contours through a network of observation points of area centroids. In the latter case, the method of interpolation affects the reliability of individual isolines and their portrayal of slope, pits and peaks.