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From: kamal on 11 Aug 2010 04:48
hi to every one, i use mathemtica for finding intersection between one
cylindrical shape by a plane but i see that answer in some piece is
wrong



range = 300000000;
intersec = {x, y, z} /.
Solve[{1*((x - y)^2 + (y - z)^2 + (z - x)^2)^2 +
1000*((x - y)^3 + (y - z)^3 + (z - x)^3)^1 == 2*(250*10^6)^4,
0 == x + y + z}, {z, y}];
p = Show[{ContourPlot3D[{1*((x - y)^2 + (y - z)^2 + (z - x)^2)^2 +
1000*((x - y)^3 + (y - z)^3 + (z - x)^3)^1 == 2*(250*10^6)^4,
0 == x + y + z}, {x, -range, range}, {y, -range,
range}, {z, -range, range}, BoundaryStyle -> None, Mesh -> None,
BoxRatios -> Automatic, PlotRange -> Automatic,
AxesLabel -> {Style[x, Large, Bold, Orange],
Style[y, Large, Bold, Orange], Style[z, Large, Bold, Orange]},
LabelStyle -> Directive[Purple, Bold], Axes -> True,
AxesStyle -> {Green, Green, Blue},
BoxStyle -> Directive[Dashed, Orange],
ContourStyle -> {{Red, Opacity[0]}, {Yellow, Opacity[0]}},
Lighting -> "Neutral", ViewPoint -> {1, 1, 1}],
ParametricPlot3D[intersec, {x, -range, range},
PlotStyle -> {Black, Black}]}]

intersec1 = {x, y, z} /.
Solve[{200*((x - y)^2 + (y - z)^2 + (z - x)^2)^4 +
4*(x - y)^2*(y - z)^2*(z -
x)^2*((x - y)^2 + (y - z)^2 + (z - x)^2) == 2*(250*10^6)^8,
0 == x + y + z}, {z, y}];
p1 = Show[{ContourPlot3D[{200*((x - y)^2 + (y - z)^2 + (z - x)^2)^4 +
4*(x - y)^2*(y - z)^2*(z -
x)^2*((x - y)^2 + (y - z)^2 + (z - x)^2) == 2*(250*10^6)^8,
0 == x + y + z}, {x, -range, range}, {y, -range,
range}, {z, -range, range}, BoundaryStyle -> None, Mesh -> None,
BoxRatios -> Automatic, PlotRange -> Automatic,
AxesLabel -> {Style[x, Large, Bold, Orange],
Style[y, Large, Bold, Orange], Style[z, Large, Bold, Orange]},
LabelStyle -> Directive[Purple, Bold], Axes -> True,
AxesStyle -> {Green, Green, Blue},
BoxStyle -> Directive[Dashed, Orange],
ContourStyle -> {{Green, Opacity[0]}, {Yellow, Opacity[0]}},
Lighting -> "Neutral", ViewPoint -> {1, 1, 1}],
ParametricPlot3D[intersec1, {x, -range, range},
PlotStyle -> {Black, Black}]}]

intersec2 = {x, y, z} /.
Solve[{2*((x - y)^2 + (y - z)^2 + (z - x)^2)^4 +
4*(x - y)^2*(y - z)^2*(z -
x)^2*((x - y)^2 + (y - z)^2 + (z - x)^2) == 2*(250*10^6)^8,
0 == x + y + z}, {z, y}];
p2 = Show[{ContourPlot3D[{2*((x - y)^2 + (y - z)^2 + (z - x)^2)^4 +
4*(x - y)^2*(y - z)^2*(z -
x)^2*((x - y)^2 + (y - z)^2 + (z - x)^2) == 2*(250*10^6)^8,
0 == x + y + z}, {x, -range, range}, {y, -range,
range}, {z, -range, range}, BoundaryStyle -> None, Mesh -> None,
BoxRatios -> Automatic, PlotRange -> Automatic,
AxesLabel -> {Style[x, Large, Bold, Orange],
Style[y, Large, Bold, Orange], Style[z, Large, Bold, Orange]},
LabelStyle -> Directive[Purple, Bold], Axes -> True,
AxesStyle -> {Green, Green, Blue},
BoxStyle -> Directive[Dashed, Orange],
ContourStyle -> {{Red, Opacity[0]}, {Yellow, Opacity[0]}},
Lighting -> "Neutral", ViewPoint -> {1, 1, 1}],
ParametricPlot3D[intersec2, {x, -range, range},
PlotStyle -> {Black, Black}]}]


if you run this commend you can see that plot diverge in some section
how can i solve that?

thank you for helping

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