Re: Area of two intersecting circles
- To: mathgroup at smc.vnet.net
- Subject: [mg123404] Re: Area of two intersecting circles
- From: Alexei Boulbitch <Alexei.Boulbitch at iee.lu>
- Date: Tue, 6 Dec 2011 03:11:39 -0500 (EST)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
I have 2 disks named A and B. They both have the same radius. Is there a function in mathematica that will find the area of the intersection between the two circles?
There is such a function. First let us look at your domain. Evaluate this:
Manipulate[
RegionPlot[
x^2 + y^2 <= 1 && (x - x0)^2 + y^2 <= r, {x, 0, 3}, {y, -1, 1},
PerformanceGoal -> "Quality"],
{x0, 0, 3}, {r, 1, 3}]
Let us define the integral:
int[x0_, r_] :=
Integrate[
Boole[x^2 + y^2 <= 1 && (x - x0)^2 + y^2 <= r], {x, 0,
x0 + r}, {y, -r, r}];
Now let us try:
int[1.9,3]
1.06324
int[2,1]
0
Have fun.
Alexei BOULBITCH, Dr., habil.
IEE S.A.
ZAE Weiergewan,
11, rue Edmond Reuter,
L-5326 Contern, LUXEMBOURG
Office phone : +352-2454-2566
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e-mail: alexei.boulbitch at iee.lu<mailto:alexei.boulbitch at iee.lu>