Re: Calculation of the surface after intersection of two

*To*: mathgroup at smc.vnet.net*Subject*: [mg100884] Re: [mg100863] Calculation of the surface after intersection of two*From*: DrMajorBob <btreat1 at austin.rr.com>*Date*: Wed, 17 Jun 2009 04:37:32 -0400 (EDT)*References*: <200906170153.VAA25938@smc.vnet.net>*Reply-to*: drmajorbob at bigfoot.com

There's a mathematical formula for this: http://mathworld.wolfram.com/Sphere-SphereIntersection.html which gives, I think, Clear[volume] volume[R_, r_, d_] = Pi/(12 d) (R + r - d)^2 (d^2 + 2 d r - 3 r^2 + 2 d R + 6 r R - 3 R^2); volume[6/10, 6/10, 1] N@% (17 \[Pi])/1500 0.0356047 Here are some of the results from the article, derived in Mathematica: volume[R, R, d] // Simplify 1/12 \[Pi] (d - 2 R)^2 (d + 4 R) volume[R, r, r + R] 0 eqn = volume[R, R, k R] == (4/3 Pi R^3)/2 // Simplify (8 - 12 k + k^3) R == 0 Array[N@Root[eqn[[1, 1]], #] &, 3] {-3.75877, 0.694593, 3.06418} d can't be negative, and if d >= 2 the spheres don't intersect, so only the second root is valid. Bobby On Tue, 16 Jun 2009 20:53:32 -0500, Horacius ReX <horacius.rex at gmail.com> wrote: > Hi, > > I have two spheres of radius 0.6 whose origins are separated a > distance of 1. So the spheres overlap and I want to calculate the > total surface now. > > For that purpose I started to calculate the surface of the separated > spheres, which is trivial and I can do by hand, but after they > intersect or overlap, how can I tell the program to calculate the > surface ? > > Thanks in advance > -- DrMajorBob at bigfoot.com

**References**:**Calculation of the surface after intersection of two spheres***From:*Horacius ReX <horacius.rex@gmail.com>