# 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 \$Assumptions assumptions to make about parameters GenerateConditions False whether to generate answers that involve conditions on parameters Method Automatic method to use WorkingPrecision Infinity the precision used in internal computations
• Specific methods for the parametrized case include:
•  Automatic automatic 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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