Re: Area of two intersecting circles
- To: mathgroup at smc.vnet.net
- Subject: [mg123386] Re: Area of two intersecting circles
- From: "Dr. Wolfgang Hintze" <weh at snafu.de>
- Date: Mon, 5 Dec 2011 05:14:56 -0500 (EST)
- Delivered-to: l-mathgroup@mail-archive0.wolfram.com
- References: <jbf968$l4j$1@smc.vnet.net>
"Scott Colwell" <srcolwell at gmail.com> schrieb im Newsbeitrag news:jbf968$l4j$1 at smc.vnet.net... >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? > You can use Boole[] to find the formula in the following way h[a_] := Integrate[Boole[(x - a)^2 + y^2 <= r^2 && (x + a)^2 + y^2 <= r^2], {x, -r, r}, {y, -r, r}, Assumptions -> {a >= 0, r > 0}] h[a] Out[12]= Piecewise[{{Pi*r^2, a == 0 && r > 0}, {Pi*r^2 - 2*a*Sqrt[-a^2 + r^2] - 2*r^2*ArcTan[a/Sqrt[-a^2 + r^2]], a > 0 && a - r < 0}}] In[13]:= h[0] Out[13]= Pi*r^2 In[14]:= h[r] Out[14]= 0 Regards, Wolfgang