圆柱体表面积计算：展开图法

GeoGebra 命令及参数

1. Shuffle(Sequence[5]) → randomList2, {2, 4, 3, 5, 1}
2. Element(randomList2, Mod[countQuestion, 5] + 1) → randomNum2
3. Shuffle(Flatten[Append[Factors[randomNum2] \ {randomNum2}, 1]]) → l3, {1, 2, 2}
4. Element(l3, 1) → Div
5. Shuffle(Sequence[2, 5]) → randomList1, {3, 5, 2, 4}
6. Element(randomList1, Mod[countQuestion, 4] + 1) → randomNum1
7. Zip(Element[legends, kk], kk, clickedSurfaces) → legendsToShow
8. Zip(Element[formulas, kk], kk, clickedSurfaces) → formulasToShow
9. If(abs(tCil) < 1, ((rCil * sin((-θCil))), ((rCil * (1 - cos((-θCil)))) * cos(ϕCil)) - (hei * sin(ϕCil)), (hei * cos(ϕCil)) + ((rCil * (1 - cos((-θCil)))) * sin(ϕCil))), ((-pi), ((-hei) * sin(ϕCil)), (hei * cos(ϕCil)))) → CE
10. If(abs(tCil) < 1, ((rCil * sin(θCil)), ((rCil * (1 - cos(θCil))) * cos(ϕCil)) - (hei * sin(ϕCil)), (hei * cos(ϕCil)) + ((rCil * (1 - cos(θCil))) * sin(ϕCil))), (pi, ((-hei) * sin(ϕCil)), (hei * cos(ϕCil)))) → CF
11. If(abs(tCil) < 1, ((rCil * sin((-θCil))), ((rCil * (1 - cos((-θCil)))) * cos(ϕCil)), ((rCil * (1 - cos((-θCil)))) * sin(ϕCil))), ((-pi), 0, 0)) → CG
12. If(abs(tCil) < 1, ((rCil * sin(θCil)), ((rCil * (1 - cos(θCil))) * cos(ϕCil)), ((rCil * (1 - cos(θCil))) * sin(ϕCil))), (pi, 0, 0)) → CH
13. Segment(CE, CG) → mCil
14. Segment(CF, CH) → nCil
15. If(abs(tCil) < 1, CurveCartesian[(rCil * sin((CLIPBOARDmagicSTRINGu * θCil))), ((rCil * (1 - cos((CLIPBOARDmagicSTRINGu * θCil)))) * cos(ϕCil)), ((rCil * (1 - cos((CLIPBOARDmagicSTRINGu * θCil)))) * sin(ϕCil)), CLIPBOARDmagicSTRINGu, -1, 1], CurveCartesian[(pi * CLIPBOARDmagicSTRINGu), 0, 0, CLIPBOARDmagicSTRINGu, -1, 1]) → lCil
16. If(abs(tCil) < 1, CurveCartesian[(rCil * sin((CLIPBOARDmagicSTRINGu * θCil))), ((rCil * (1 - cos((CLIPBOARDmagicSTRINGu * θCil)))) * cos(ϕCil)) - (hei * sin(ϕCil)), (hei * cos(ϕCil)) + ((rCil * (1 - cos((CLIPBOARDmagicSTRINGu * θCil)))) * sin(ϕCil)), CLIPBOARDmagicSTRINGu, -1, 1], CurveCartesian[(pi * CLIPBOARDmagicSTRINGu), ((-hei) * sin(ϕCil)), (hei * cos(ϕCil)), CLIPBOARDmagicSTRINGu, -1, 1]) → jCil
17. If(abs(tCil) < 1, Surface[(rCil * sin((CLIPBOARDmagicSTRINGu * θCil))), ((rCil * (1 - cos((CLIPBOARDmagicSTRINGu * θCil)))) * cos(ϕCil)) - (CLIPBOARDmagicSTRINGv * sin(ϕCil)), (CLIPBOARDmagicSTRINGv * cos(ϕCil)) + ((rCil * (1 - cos((CLIPBOARDmagicSTRINGu * θCil)))) * sin(ϕCil)), CLIPBOARDmagicSTRINGu, -1, 1, CLIPBOARDmagicSTRINGv, 0, hei], Surface[(pi * CLIPBOARDmagicSTRINGu), ((-CLIPBOARDmagicSTRINGv) * sin(ϕCil)), (CLIPBOARDmagicSTRINGv * cos(ϕCil)), CLIPBOARDmagicSTRINGu, -1, 1, CLIPBOARDmagicSTRINGv, 0, hei]) → iCil
18. Rotate(Rotate[eCil, ϕCil, Line[CC, xAxis]], ϕCil, xAxis) → topCil
19. Circle((0, 1, 0), 1, xOyPlane) → baseCil
20. Circle((0, 1, 0), 1, xOyPlane) → baseCil2
21. Segment((0, 1, 0), (1, 1, 0)) → segRad
22. TableText(formulas) → text1
23. Polygon({((-pi), 0, 0), (pi, 0, 0), (pi, (-hei), 0), ((-pi), (-hei), 0)}) → unfoldedCilinder
24. Translate(baseCil2, Vector[(-(0, 2 + hei))]) → baseCil2'
25. Zip(Element[formulasR, kk], kk, clickedSurfaces) → formulasToShowR
26. Append("\phantom{=}", Sequence["=", ii, 1, Length[formulasToShow] - 1]) → equalSigns
27. TableText(formulasToShowR, "r") → completeTable
28. Text("\textsf{Click all sections of the net}", (-3.1, 4.8), true, true, -1, 1) → onboardingSurfaces
29. Vector(G, H) → onboardingSegmentArrow1
30. PointIn(baseCil2) → I
31. Vector(G, I) → onboardingSegmentsArrow2
32. Text(SADyn, B, true, true, -1, -1) → text8
33. Zip(If[kk ≟ 2, ((2 * input1) * input2), kk ≟ 1, 0, input1^(2)], kk, clickedSurfaces) → l1
34. Corner(5) → L
35. Vector(E, F) → onboardingSurfaceArrow
36. TableText(legendsToShow, Sequence["\hspace{110}\vspace{10}", kk, 1, Length[formulasToShow]], formulasToShow, "vlcr") → tableLeft
37. TableText({(("\color{" * colorBlue) * "}\rule{35mm}{0.5mm}"), "\hspace{20}", (("\color{" * colorBlue) * "}\rule{45mm}{0.5mm}")}, {(("\color{" * colorBlue) * "}\textsf{Surface Area =}"), "", formulaBelowTable}, "lcr") → belowTable
38. Corner(5) → A
39. Text("\textsf{Click one}", G + (-0.5, 1), true, true) → onboardingSegments