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:
-
AccuracyGoal Infinity digits of absolute accurary sought Assumptions $Assumptions assumptions to make about parameters GenerateConditions Automatic whether to generate conditions on parameters PerformanceGoal $PerformanceGoal aspects of performance to try to optimize PrecisionGoal Automatic digits of precision sought WorkingPrecision Automatic the precision used in internal computations - Perimeter can be used with symbolic regions in GeometricScene.
Examples
open allclose allBasic Examples (4)
Scope (14)
Special Regions (4)
Formula Regions (4)
The perimeter of a disk represented as an ImplicitRegion:
The perimeter of a disk represented as a ParametricRegion:
Using a rational parametrization of a disk:
The perimeter of an ImplicitRegion:
The perimeter of a ParametricRegion:
Mesh Regions (3)
The perimeter of a BoundaryMeshRegion:
The perimeter of a MeshRegion:
The perimeter of a MeshRegion with mixed dimensions:
Derived Regions (2)
Options (2)
WorkingPrecision (1)
Compute the Perimeter using machine arithmetic:
Applications (4)
A farmer has a 40.5-acre plot of land in the shape of a regular pentagon. How much fence is needed to enclose the plot?
Model the plot as a RegularPolygon of unknown radius:
Determine the radius given the area:
Find the perimeter of a MengerMesh in [0,1]×[0,1]:
Find the general formula for the perimeter of a MengerMesh of order n:
The perimeter tends to infinity even though the regions stay bounded inside [0,1]×[0,1]:
Compute the orbital circumference of Mars:
The coastline paradox states a country's border is fractal in nature and hence its perimeter is unbounded [more info].
Obtain the polygon representing the United Kingdom:
The perimeter of the United Kingdom with various amounts of sampling points along its border:
Properties & Relations (3)
For regions with only full-dimensional components, the perimeter is the ArcLength of its boundary:
Regions with nonzero perimeter will have nonzero Area:
Find the perimeter of lamina entities:
Use EntityValue to find the perimeter of a salinon with outer radius 5 and inner radius 1:
Find the perimeter through the region's implicit representation:
Possible Issues (1)
Text
Wolfram Research (2017), Perimeter, Wolfram Language function, https://reference.wolfram.com/language/ref/Perimeter.html (updated 2019).
CMS
Wolfram Language. 2017. "Perimeter." Wolfram Language & System Documentation Center. Wolfram Research. Last Modified 2019. https://reference.wolfram.com/language/ref/Perimeter.html.
APA
Wolfram Language. (2017). Perimeter. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/Perimeter.html