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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.
Aug 10, 2020 · This video introduces level curves, or contours, and how we graph them in two dimensions to represent three-dimensional surfaces.
- 15 min
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- Math with Dr. Claire
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.
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.
A contour diagram is, in essence, a \topographical map" of the graph of z = f(x; y). 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.
Sep 29, 2023 · Topographical maps can be used to create a three-dimensional surface from the two-dimensional contours or level curves. For example, level curves of the distance function defined by \(f(x,y) = \frac{x^2 \sin(2y)}{32}\) plotted in the \(xy\)-plane are shown at left in Figure \(\PageIndex{8}\).
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Jul 19, 2011 · How Do I Calculate Slope (or Gradient) in the Geosciences? Gradient in the case of hillslope and water table is just like calculating the slope of a line on a graph: "rise" over "run." But how do you do that using a contour (or topographic) map?
