Arc

Author

Eric W. Weisstein
June 11, 2015

This notebook downloaded from http://mathworld.wolfram.com/notebooks/PlaneGeometry/Arc.nb.

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/Arc.html.

©2015 Wolfram Research, Inc. except for portions noted otherwise

Eric W. Weisstein
January 11, 2002

For more information, see Eric's MathWorld entry http://mathworld.wolfram.com/Arc.html.

Plots

ParametricPlot

ParametricPlot[{Cos[t],Sin[t]},{t,-#/2,#/2},AspectRatio->Automatic,AxesOrigin->{0,0},Ticks->None,PlotRange->1.01]&/@{.2,.5,1}

ContourPlot

Block[{p=1,a=1},ContourPlot[x^2+y^2==a^2,{x,-1,1},{y,-1,1},RegionFunction->Function[{x,y},-p/2≤ArcTan[x,y]≤p/2]]]

Properties

Three Arcs

p=Table[{Cos[#],Sin[#]}&[2Pi(n-1/4)/3],{n,0,2}]

Show[Graphics[{PointSize[.08],Point/@p},AspectRatio->Automatic],PlotRange->All]

ineqs=Function[v,v.v][{x,y}-#]<1&/@p

Show[InequalityPlot[#,{x,-2,2},{y,-2,2},DisplayFunction->Identity]&/@Partition[ineqs,2,1,1],PlotRange->All,DisplayFunction->$DisplayFunction]