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A topographical map contains curved lines called contour lines. Each contour line corresponds to the points on the map that have equal elevation (Figure 1). A level curve of a function of two variables [latex]f\,(x,\ y)[/latex] is completely analogous to a counter line on a topographical map.
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Level curves are the equivalent of contours on a topographical map. In such a map the terrain is shown by drawing curves through all points which have the same height above sea level. The numbers on the curves in the map shown below are the heights above sea level in metres.
A topographical map is a two-dimensional visualization of three-dimensional terrain through the so-called level curves or contours corresponding to points of equal elevation. Example 1. Here is a map of the region near South Hamilton, NY: (a) If you are standing where the black dot is, how high are you? What do you see when you look south?
If you have seen a topographic map then you have seen a contour plot. Example: To illustrate this we first draw the graph of z = x2 + y2. On this graph we draw contours, which are curves at a fixed height z = constant. For example the curve at height z = 1 is the circle x2 + y2 = 1.
Aug 31, 2019 · Constructing a topographic map by drawing in contours can be easily done if a person remembers the following rules regarding contour lines: Contour lines represent lines connecting points of equal elevation above sea level; Contour lines never cross, split, or die off
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3.3 Level Curves and Level Surfaces. Topographic (also called contour) maps are an effective way to show the elevation in 2-D maps. These maps are marked with contour lines or curves connecting points of equal height. Figure 1: Topographic map of Stowe, Vermont, in the US.
