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Cylinder Net with Slider

Cylinder Net with Slider
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2024-06-06 18:12
CirclePolygonSolid GeometryTransformationSlider Animation
① This example demonstrates the dynamic unfolding and rolling of a cylinder's surface using sliders, showing how a cylinder consists of a rectangular lateral face and two circular bases. ② Core mathematical concepts include solid geometry, cylinder nets, surface area, and the effect of parameter changes on the 3D shape. ③ Construction highlights: using GeoGebra commands such as Cylinder, Slider, Rotate, Translate, Dilate, Polygon, CircleArc, Surface, Intersect, Midpoint, and Mirror to create the cylinder and its net, with interactive sliders for radius (r) and height (h) to animate the transformation. ④ Suitable for middle and high school geometry classes, math labs, or exploratory learning to visualize the relationship between 3D solids and their 2D nets.

GeoGebra Commands & Parameters

  1. Cylinder(A, C, r) → a, c, d, b
  2. Line(D, E) → f
  3. Intersect(f, d, 1) → F
  4. Sphere(F, r) → e
  5. Intersect(f, e) → G, H
  6. Plane(G, F, C) → g
  7. Rotate(C, If[0 < i ≤ 1, (i * pi / 2), pi / 2], D, g) → C'
  8. Rotate(d, If[0 < i ≤ 1, (i * pi / 2), pi / 2], D, g) → d'
  9. Rotate(dd, If[0 < i ≤ 1, (i * pi / 2), pi / 2], D, g) → dd'
  10. Dilate(C, If[1 < i ≤ 2, 2 - i, 0], I) → C'_1
  11. Dilate(C, If[1 < i ≤ 2, 2 - i, 0], J) → C'_2
  12. Vector(C, C'_1) → u
  13. Vector(C, C'_2) → v
  14. Translate(dd, u) → dd'_1
  15. Translate(dd, v) → dd'_2
  16. Translate(K, u) → K'
  17. Translate(K, v) → K'_1
  18. Rotate(K', If[1 < i ≤ 2, ((i - 1) * pi), pi], C'_1) → K''
  19. Rotate(K'_1, If[1 < i ≤ 2, ((-(i - 1)) * pi), (-pi)], C'_2) → L
  20. Translate(D, u) → D'
  21. Translate(D, v) → D'_1
  22. Polygon(D', D'_1, N, M) → poly1, d'_1, d'_2, n, m
  23. Segment(K'', Q) → j
  24. CircleArc(P, Q, M) → k
  25. Segment(L, S) → l
  26. CircleArc(R, N, S) → p
  27. CircleArc(C'_2, D'_1, L) → q
  28. CircleArc(C'_1, K'', D') → s
  29. Plane(T, A, B) → o
  30. Rotate(C', If[2 < i ≤ 3, ((i - 2) * pi / 2), pi / 2], E, g) → C''
  31. Rotate(poly1, If[2 < i ≤ 3, ((i - 2) * pi / 2), pi / 2], E, g) → poly1'
  32. Rotate(d', If[2 < i ≤ 3, ((i - 2) * pi / 2), pi / 2], E, g) → d'_3
  33. Rotate(dd', If[2 < i ≤ 3, ((i - 2) * pi / 2), pi / 2], E, g) → dd'_3
  34. Rotate(K'', If[2 < i ≤ 3, ((i - 2) * pi / 2), pi / 2], E, g) → K'''
  35. Rotate(Q, If[2 < i ≤ 3, ((i - 2) * pi / 2), pi / 2], E, g) → Q'
  36. Segment(K''', Q') → j'
  37. Rotate(L, If[2 < i ≤ 3, ((i - 2) * pi / 2), pi / 2], E, g) → L'
  38. Rotate(S, If[2 < i ≤ 3, ((i - 2) * pi / 2), pi / 2], E, g) → S'
  39. Segment(L', S') → l'
  40. Dilate(C'', If[3 < i ≤ 4, 4 - i, 0], U) → C'''
  41. Vector(C'', C''') → w
  42. Dilate(C'', If[3 < i ≤ 4, 4 - i, 0], V) → C'''_1
  43. Vector(C'', C'''_1) → t
  44. Translate(Z, w) → Z'
  45. Translate(Z, t) → Z'_1
  46. Translate(W, w) → W'
  47. Translate(W, t) → W'_1
  48. Rotate(W', If[3 < i ≤ 4, ((-(i - 3)) * pi), (-pi)], C''') → W''
  49. CircleArc(C''', Z', W'') → c_1
  50. Segment(Z, Z') → f_1
  51. Rotate(W'_1, If[3 < i ≤ 4, ((i - 3) * pi), pi], C'''_1) → A_1
  52. CircleArc(C'''_1, Z'_1, A_1) → d_1
  53. Segment(Z, Z'_1) → g_1
  54. Segment(R, N) → h_1
  55. Angle(N, R, S) → α
  56. CurveCartesian(x(C'_2) + (r * cos(t)), y(C'_2) + (r * sin(t)), z(C'_2), t, pi / 2, pi / 2 + α) → a_1
  57. Vector(A, C) → tt
  58. Surface(x(C'_2) + (r * cos(t)) - (u * x(tt)), y(C'_2) + (r * sin(t)) - (u * y(tt)), z(C'_2) - (u * z(tt)), u, 0, 1, t, pi / 2, pi / 2 + α) → b_1
  59. Surface((-x(C'_2)) - (r * cos(t)) - (u * x(tt)), y(C'_2) + (r * sin(t)) - (u * y(tt)), z(C'_2) - (u * z(tt)), u, 0, 1, t, pi / 2, pi / 2 + α) → e_1
  60. Midpoint(L', S') → B_1
  61. Midpoint(K''', Q') → C_1
  62. Line(B_1, C_1) → i_1
  63. Mirror(d_1, i_1) → k_1
  64. Mirror(c_1, i_1) → p_1
  65. Mirror(Z, i_1) → Z'_2
  66. Mirror(Z', i_1) → Z''
  67. Segment(Z'_2, Z'') → j_1
  68. Mirror(Z, i_1) → Z'_3
  69. Mirror(Z'_1, i_1) → D_1
  70. Segment(Z'_3, D_1) → l_1

AI Drawing Prompt Reference

Draw a cylinder net with two circular bases and a rectangular side. Use sliders to adjust the radius and height of the cylinder, and demonstrate how the cylinder unfolds into a 2D shape through rotations, translations, and dilations. Start by creating the cylinder, then generate its net, and finally control the cylinder's shape changes with the sliders.
The prompt above was compiled from the original drawing commands and is for reference only.