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A 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. [1][2] It is a plane section of the three-dimensional graph of the function parallel to the -plane. More generally, a contour line for a function of ...
- Formal Definition
- Contours and Gradients
- Contour Surfaces and Gradients
Let z = f(x,y) be a function of two variables that forms a curved surface in the 3D coordinate plane. If a plane z = k, where k is some constant, intersects the surface, a contour with the equation k = f(x, y) is formed. These curves are also referred to as level curves since their distance from the xy-plane is k for any point on the plane. The gra...
There is a special relationship between the contour map and the gradientfield for a function of several variables. Consider the following topographic map: Suppose that you are on some hilly terrain represented by the above topographic map. You start at point E, which is on the level curve with an elevation of 200 feet. You want to climb the shortes...
The relationship between a gradient field and contour map for a function of three variables is as follows. Given that w = f(x, y, z) is a function of three variables, then the gradient of f is given by: Let k be some constant, then k = f(x, y, z) is the level surface for f (as compared to a level curve for z = f(x, y)). The level surface is also re...
Aug 24, 2024 · 2. Contour lines are always a uniform vertical distance apart, called a contour interval, which is stated on the map (bottom middle). Contour lines never branch, fork, or cross one another. Contour lines form a “V” when crossing a stream valley; the bottom of the “V” always points upstream, so the water flows in the opposite direction.
Interpreting Contour Plots - Examples - 1 Useful Properties of Contour Plots If the contour lines are evenly spaced in their z values, contour lines closer together indicate more rapid change/steeper slopes. contour lines further apart indicate atter regions. peaks and valleys look the same; only the values of the contours let you distinguish them.
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Aug 31, 2019 · If the topographic map in Figure 3.6 has a fractional scale of 1:12,000 then 1 inch is equal to 12,000 inches or 1000ft; this 1inch = 1000ft equivalency is for the horizontal scale. When we hold a ruler to the y-axis of the topographic profile in Figure 3.6, we see that 0.5 inches = 50ft, which means 1 inch = 100ft on the vertical scale.
Part 6: Contour Lines. A contour line (also known as a level curve) for a given surface is the curve of intersection of the surface with a horizontal plane, z = c. A representative collection of contour lines, projected onto the xy -plane, is a contour map or contour plot of the surface. In particular, if the surface is the graph of a function ...
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The gure below shows how the contour diagram from the corn production example is related to the graph of the corn production function C= f(R;T). Contour lines, or level curves, are obtained from a surface by slicing it with horizontal planes. A contour diagram is a collection of level curves labeled with function values.
