Math 2.0

concept

Contour line

Summary

A contour line of a function ff of two real variables is a curve in the plane along which ff has a constant value cc. It is a level set {(x,y):f(x,y)=c}\{(x, y) : f(x, y) = c\} of ff, drawn in the (x,y)(x, y)-plane. A contour map draws the contour lines for several equally spaced values of cc. It shows the shape of the graph of ff in the plane.

Remarks

On a topographic map, ff is the height above sea level, and the contour lines join points of equal height. Where the contour lines of equally spaced values are close together, the function changes fast.

Explanations

L1 human

Imagine that you cut a hill with horizontal planes at heights 1010, 2020, 3030 and so on, and you look at the cuts from above. Each cut gives a closed curve on the map, and these curves are the contour lines.

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Euclidean space, object, no evidence levelEuclidean spaceobjectFunction, concept, no evidence levelFunctionconceptGraph of a function, concept, no evidence levelGraph of a functionconceptFunction of several variables, concept, no evidence levelFunction of several v…conceptLevel set, concept, no evidence levelLevel setconceptContour line, concept, no evidence levelContour lineconcept
Each node uses the nodes above it. The colour of the bar on a box shows the evidence level, and the box also gives it as text. The list below has the same nodes.
  • no evidence level
  1. Euclidean space object
  2. Function concept
  3. Graph of a function concept
  4. Function of several variables concept
  5. Level set concept
  6. Contour line concept

Sources

  1. Web https://en.wikipedia.org/wiki/Contour_line, lead section

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