Dandeline Spheres and Parabola
Author
Alejandro Latorre Chirot
Title
Dandeline Spheres and Parabola
Description
Animation that shows parabola case in Dandeline Spheres
Category
Working Material
Keywords
Dandeline Spheres, Parabola
URL
http://www.notebookarchive.org/2024-03-2ck5v4l/
DOI
https://notebookarchive.org/2024-03-2ck5v4l
Date Added
2024-03-05
Date Last Modified
2024-03-05
File Size
351.74 kilobytes
Supplements
Rights
Redistribution rights reserved
Download
Open in Wolfram Cloud
Dandeline Spheres And Parabola
Dandeline Spheres And Parabola
Alejandro Latorre Chirot
In[]:=
DandelineSpheres::usage="Esfera tangente a un plano paralelo a la generatriz y a un cono, su punto de contacto con el plano determina ei foco de una parábola en el espacio formada por la intersección del plano y el cono. Las distancias PF y Pl (punto a directriz) deben ser iguales, pero el foco es una aproximación. Las distancias prácticamente son iguales. Aquí utilice mi función γ[t]. Referencia: De internet, LibreTexts, K12 EDUCATION, Dandelin and the parabola. ";l2[t_]:={0.556t,-1.8201,4.02656};k[x_,y_]:=4.02656;j[x_,y_]:=2.78y+9.086436140;a1=0;b1=2.78;c1=-1;d11=-9.086436140;γ[t_]:=(d11/(a1Cos[t]+b1Sin[t]+2.78c1))Cos[t],(d11/(a1Cos[t]+b1Sin[t]+2.78c1))Sin[t],d11Cos[t]+Sin[t]+c1;ζ[t_]:={1.4484Cos[t],1.4484Sin[t],4.02656};DoQP={0,-1.8201,4.02656}-γ[t];PC=Cross[QP,{0.556,0,0}];N1=Norm[PC];N2=Norm[{0.556,0,0}];d4[t_]:=N[Norm[{-0.000737292,-1.44702,5.06372}-γ[t]]];d5[t_]:=N;p=Grid[{{PF,Pl},{d4[t],d5[t]}},FrameAll];Print[p],t,-1.05π,,0.1;
a1
2.78
b1
2.78
N1
N2
π
7
PF | Pl |
7.17171 | 7.16801 |
PF | Pl |
5.96516 | 5.96149 |
PF | Pl |
4.98363 | 4.97999 |
PF | Pl |
4.17695 | 4.17335 |
PF | Pl |
3.50848 | 3.50491 |
PF | Pl |
2.95095 | 2.94742 |
PF | Pl |
2.4838 | 2.48031 |
PF | Pl |
2.09129 | 2.08785 |
PF | Pl |
1.76129 | 1.75787 |
PF | Pl |
1.48431 | 1.48093 |
PF | Pl |
1.25295 | 1.24959 |
PF | Pl |
1.06138 | 1.05803 |
PF | Pl |
0.905049 | 0.901677 |
PF | Pl |
0.780394 | 0.776974 |
PF | Pl |
0.684696 | 0.68119 |
PF | Pl |
0.615933 | 0.612293 |
PF | Pl |
0.572676 | 0.56886 |
PF | Pl |
0.554031 | 0.550006 |
PF | Pl |
0.559593 | 0.555352 |
PF | Pl |
0.589445 | 0.585006 |
PF | Pl |
0.644167 | 0.639567 |
PF | Pl |
0.724866 | 0.720151 |
PF | Pl |
0.833228 | 0.828441 |
PF | Pl |
0.971588 | 0.966766 |
PF | Pl |
1.14303 | 1.1382 |
PF | Pl |
1.35155 | 1.34673 |
PF | Pl |
1.60224 | 1.59745 |
PF | Pl |
1.9016 | 1.89683 |
PF | Pl |
2.25788 | 2.25315 |
PF | Pl |
2.68165 | 2.67695 |
PF | Pl |
3.18652 | 3.18186 |
PF | Pl |
3.79018 | 3.78556 |
PF | Pl |
4.51589 | 4.51131 |
PF | Pl |
5.39466 | 5.39012 |
PF | Pl |
6.46851 | 6.46399 |
PF | Pl |
7.79541 | 7.79094 |
PF | Pl |
9.45719 | 9.45274 |
PF | Pl |
11.5721 | 11.5677 |
In[]:=
AnimateShowsurf1=ParametricPlot3DCos[u],Sin[u],v,{u,0,2π},{v,-20,20},PlotStyleDirective[Green,Specularity[White,20],Opacity[0.1]],MeshFalse,surf3=ParametricPlot3D[{1.53779Cos[u]Sin[v],1.53779Sin[u]Sin[v],1.53779Cos[v]+4.54321},{u,0,2π},{v,0,π},ColorFunction"LightTemperatureMap",MeshFalse],surf4=Plot3D[j[x,y],{x,-5,5},{y,-5,5},PlotStyleDirective[Yellow,Specularity[White,20],Opacity[0.2]],MeshFalse],surf5=Plot3D[k[x,y],{x,-5,5},{y,-5,5},PlotStyleDirective[Red,Specularity[White,20],Opacity[0.2]],MeshFalse],curv1=ParametricPlot3D[γ[t],{t,-1.05π,θ1},ColorFunctionFunction[{x,y,z},Hue[z]]],curv2=ParametricPlot3D[ζ[θ],{θ,0,2π}],Graphics3D[Tube[{l2[-10],l2[10]},0.07]],Graphics3D[{Black,Ball[{-0.000737292,-1.44702,5.06372},0.16]}],Graphics3D[{Red,Ball[N[γ[t]],0.18]/.tθ1}],Graphics3D[{Black,Ball[N[l2[t+5]],0.18]/.t3.2θ1}],Graphics3D[{Black,Dashed,Line[{N[γ[t]]/.tθ1,{-0.000737292,-1.44702,5.06372}}]}],Graphics3D[{Black,Dashed,Line[{N[γ[t]]/.tθ1,l2[t+5]/.t3.2θ1}]}],AxesLabel->(Style[#,15,Blue]&/@{"X","Y","Z"}),AxesOrigin{0,0,0},MeshFalse,AxesTrue,BoxedFalse,PlotRangeAll,PerformanceGoal"Quality",{θ1,-π,π/7,0.1},AnimationRunningFalse
v
2.78
v
2.78
Out[]=
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Cite this as: Alejandro Latorre Chirot, "Dandeline Spheres and Parabola" from the Notebook Archive (2024), https://notebookarchive.org/2024-03-2ck5v4l
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