Re: Getting only 1 of 3 curves of intersection

*To*: mathgroup at smc.vnet.net*Subject*: [mg126313] Re: Getting only 1 of 3 curves of intersection*From*: Andrzej Kozlowski <akozlowski at gmail.com>*Date*: Mon, 30 Apr 2012 04:43:02 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*References*: <201204290609.CAA10817@smc.vnet.net>

Try this: g1 = Plot3D[Sin[x*y], {x, 0, Pi}, {y, 0, Pi}, PlotStyle -> None, MeshStyle -> Red, Axes -> True, AxesLabel -> {"x", "y", "z"}]; g2 = Plot3D[Cos[x*y], {x, 0, Pi}, {y, 0, Pi}, Mesh -> None, PlotStyle -> {Cyan, Opacity[.8]}]; sols1 = w /. Solve[Sin[w] == Cos[w] && 0 < w < Pi^2, w, Reals] // N; sols2 = Flatten[Solve[{z == Sin[#], x y == #}, {y, z}] & /@ sols1, 1]; g3 = ParametricPlot3D[{x, y, z} /. sols2, {x, 0, Pi}, PlotStyle -> {Magenta, Thickness[.007]}]; Show[g1, g2, g3, Background -> LightYellow, ImageSize -> 500] Andrzej Kozlowski On 29 Apr 2012, at 08:09, Bill wrote: > Hi: > > Consider the following plot: > > g1=Plot3D[Sin[x*y],{x,0,Pi},{y,0,Pi},PlotStyle->None,MeshStyle->Red,Axes->True,AxesLabel->{"x","y","z"}]; > g2=Plot3D[Cos[x*y],{x,0,Pi},{y,0,Pi},Mesh->None,PlotStyle->{Cyan,Opacity[.8]}]; > nsSol=NSolve[{z-Sin[x*y],z-Cos[x*y]},{y,z}];//Quiet > g3=ParametricPlot3D[{x,y,z}/.nsSol[[2]],{x,0,Pi},PlotStyle->{Magenta,Thickness[.007]}]; > Show[g1,g2,g3,Background->LightYellow,ImageSize->500] > > Using the above Mathematica 8.0.4 code, I can plot one curve of intersection shown in magenta. > Within the plotted area, I can see 2 more places where intersection curves should be. > I've tried using Reduce in place of NSolve, but can't get it to work. > > Question: If this can be done, can someone please give me the code? > > > Thanks, > > Bill >

**References**:**Getting only 1 of 3 curves of intersection***From:*Bill <WDWNORWALK@aol.com>