Math 2.0

Real functions Concept

Contour line

Builds on Level setGraph of a function

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.

Reading path

To understand this page from the ground up, read these 6 pages in order. The foundations come first.

Show the path as a graph
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 page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • 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

Further reading

  1. Web https://en.wikipedia.org/wiki/Contour_line, lead section
About this page
Tag0QD83RAN8G
URIm2://0QD83RAN8G
Aliasesisoline, contour-map, level-curve-of-a-graph
Kindconcept
WritingW1 stated
MSC26B99
SpecializesLevel set
UsesLevel set, Graph of a function
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