Perimeter

Perimeter[reg]

gives the perimeter of the two-dimensional region reg.

Perimeter[{x1,x2},{s,smin,smax},{t,tmin,tmax}]

gives the perimeter of the parametrized region whose Cartesian coordinates xi are functions of s and t.

Perimeter[{x1,x2},{s,smin,smax},{t,tmin,tmax},chart]

interprets the xi as coordinates in the specified coordinate chart.

Details and Options

  • Perimeter is also known as circumference.
  • Coordinate charts in the fourth argument of Perimeter can be specified as triples {coordsys,metric,dim} in the same way as in the first argument of CoordinateChartData. The short form in which dim is omitted may be used.
  • The following options can be given:
  • Assumptions$Assumptionsassumptions to make about parameters
    GenerateConditionsFalsewhether to generate answers that involve conditions on parameters
    MethodAutomaticmethod to use
    WorkingPrecisionInfinitythe precision used in internal computations
  • Specific methods for the parametrized case include:
  • Automaticautomatic method selection
    "Integrate"exact symbolic integration
    "NIntegrate"numeric integration
  • Additional method suboptions can be given in the form Method->{,opts}.
  • Any option of Integrate or NIntegrate can be passed as a method suboption to the corresponding method.
  • Symbolic limits of integration are assumed to be real and ordered. Symbolic coordinate chart parameters are assumed to be in range given by the "ParameterRangeAssumptions" property of CoordinateChartData.

Examples

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Basic Examples  (5)

The perimeter of a disk:

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The perimeter of a 3-4-5 triangle:

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The perimeter of an annulus with inner radius 1 and outer radius 2:

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The perimeter of a sector expressed in polar coordinates:

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The perimeter of a region of dimension zero or one is 0:

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Scope  (14)

Options  (6)

Applications  (4)

Properties & Relations  (3)

Possible Issues  (2)

Neat Examples  (3)

See Also

ArcLength  Area  Volume  RegionMeasure  RegionCentroid  RegionMoment  Integrate  NIntegrate  RegionBoundary

Introduced in 2017
(11.1)