In 1701, Edmond Halley used such lines (isogons) on a chart of magnetic variation. The oldest known isobath (contour line of constant depth) is found on a map dated 1584 of the river Spaarne, near Haarlem, by Dutchman Pieter Bruinsz. The idea of lines that join points of equal value was rediscovered several times. History Edmond Halley's New and Correct Chart Shewing the Variations of the Compass (1701) In the latter case, the method of interpolation affects the reliability of individual isolines and their portrayal of slope, pits and peaks.
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 the estimated surface elevations, as when a computer program threads contours through a network of observation points of area centroids. The configuration of these contours allows map readers to infer the relative gradient of a parameter and estimate that parameter at specific places. A level set is a generalization of a contour line for functions of any number of variables.Ĭontour 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. When the lines are close together the magnitude of the gradient is large: the variation is steep. The gradient of the function is always perpendicular to the contour lines. The contour interval of a contour map is the difference in elevation between successive contour lines. A contour map is a map illustrated with contour lines, for example a topographic map, which thus shows valleys and hills, and the steepness or gentleness of slopes. In cartography, a contour line (often just called a "contour") joins points of equal elevation (height) above a given level, such as mean sea level. More generally, a contour line for a function of two variables is a curve connecting points where the function has the same particular value. It is a plane section of the three-dimensional graph of the function f ( x, y ) f(x,y) parallel to the ( x, y ) (x,y) -plane. A two-dimensional contour graph of the three-dimensional surface in the above picture.Ī contour line (also isoline, isopleth, isoquant or isarithm) of a function of two variables is a curve along which the function has a constant value, so that the curve joins points of equal value.
A three-dimensional surface, whose contour graph is below. The curve at the top represents the values along that straight line.
The bottom part of the diagram shows some contour lines with a straight line running through the location of the maximum value. For more meanings of the word "contour", see Contour (disambiguation). The class would then answer for successively higher elevations at a selected contour interval (10, 20, 30 etc.), and discuss contour intervals and line placement.This article is about lines of equal value in maps and diagrams.
With the top attached map, the class could answer for 0 (sea level), and then discuss the concept of sea level as a base elevation for contour maps. Students can be provided with a paper copy of the map on which to record their answers and draw in the contour lines with the class when the clicker portion concludes, students can be directed to complete the map and submit it for assessment. The clicker activity can stop when the answers displayed are in the appropriate location. The class then answers for successively higher elevations at a selected contour interval, and discusses line placement and related topics such as contour intervals after each iteration. The resulting display of results will show multiple points across the map and illustrate the location of the contour line. ×Display the attached map of elevation points (or a similar map) and ask students to click on a specific elevation and a contour line of that value (ie.
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