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使用单位立方体创建棱柱

使用单位立方体创建棱柱
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2020-03-04 08:13
多边形向量三角函数立体几何几何作图
①本范例演示如何使用单位立方体创建棱柱，帮助学生理解体积概念；②涉及的核心数学概念包括体积、多边形、公倍数与最大公约数、余弦定理、三维向量、线段等；③作图要点：运用了Intersect（交集）、Vector（向量）、Segment（线段）、Line（直线）、Point（点）、Polygon（多边形）、Translate（平移）、Sequence（序列）等GeoGebra命令与对象；④适合初中及以上学生，用于立体几何教学和体积概念深化。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → H
  2. Vector(H, I) → u
  3. Segment(D, C) → b
  4. Segment(C, F) → f
  5. Segment(D, G) → g
  6. Segment(G, F) → h
  7. Segment(F, E) → i
  8. Line(E, F) → j
  9. Line(H, j) → k_1
  10. Segment(E, B) → a
  11. Segment(B, C) → c
  12. Point(yAxis) → A
  13. Vector(H, A) → v
  14. Vector(H, J) → w
  15. Polygon(B, C, F, E) → çokgen1, b_1, c_1, f_1, e_1
  16. Polygon(C, D, G, F) → çokgen2, c_2, d_1, g_1, f_2
  17. Polygon(B, K, D, C) → çokgen3, b_2, k_2, d, c_3
  18. Translate(B, u) → B'
  19. Translate(K, u) → K'
  20. Translate(D, u) → D'
  21. Translate(C, u) → C'
  22. Intersect(j, f) → L
  23. Intersect(g, h) → M
  24. Line(L, M) → q
  25. Translate(B, w) → B'_1
  26. Translate(K, w) → K'_1
  27. Translate(D, w) → D'_1
  28. Translate(C, w) → C'_1
  29. Translate(B', w) → B''
  30. Translate(K', w) → K''
  31. Translate(D', w) → D''
  32. Translate(C', w) → C''
  33. Translate(B'', w) → B'''
  34. Translate(K'', w) → K'''
  35. Translate(D'', w) → D'''
  36. Translate(C'', w) → C'''
  37. Translate(B''', w) → N
  38. Translate(K''', w) → O
  39. Translate(D''', w) → P
  40. Translate(C''', w) → Q
  41. Translate(N, w) → N'
  42. Translate(O, w) → O'
  43. Translate(P, w) → P'
  44. Translate(Q, w) → Q'
  45. Translate(B'', w) → B'''_1
  46. Translate(K'', w) → K'''_1
  47. Translate(D'', w) → D'''_1
  48. Translate(C'', w) → C'''_1
  49. Translate(B'''_1, w) → R
  50. Translate(K'''_1, w) → S
  51. Translate(D'''_1, w) → T
  52. Translate(C'''_1, w) → U
  53. Translate(R, w) → R'
  54. Translate(S, w) → S'
  55. Translate(T, w) → T'
  56. Translate(U, w) → U'
  57. Intersect(j, q) → V
  58. Intersect(b, f) → W
  59. Intersect(b_2, k_2) → Z_1
  60. Intersect(b_2, k_2) → K_1
  61. Translate(C, w) → C'_2
  62. Translate(D, w) → D'_2
  63. Translate(G, w) → G'
  64. Translate(F, w) → F'
  65. Sequence(Polygon[Translate[B, Vector[(i * u)]], Translate[K, Vector[(i * u)]], Translate[D, Vector[(i * u)]], Translate[C, Vector[(i * u)]]], i, 1, k - 1) → liste3
  66. Sequence(Translate[Element[liste1, 1], Vector[(i * u)]], i, 1, k - 1) → liste4
  67. Sequence(Polygon[Translate[B, Vector[(i * u)]], Translate[C, Vector[(i * u)]], Translate[F, Vector[(i * u)]], Translate[E, Vector[(i * u)]]], i, 1, k - 1) → liste5
  68. Sequence(Segment[Translate[F, Vector[(u * i)]], Translate[E, Vector[(u * i)]]], i, 0, k - 1) → liste10
  69. Sequence(Translate[liste10, Vector[(v * i)]], i, 1, o - 1) → liste11
  70. Sequence(Segment[Translate[G, Vector[(w * i)]], Translate[F, Vector[(w * i)]]], i, 0, m - 1) → liste12
  71. Sequence(Translate[liste12, Vector[(v * i)]], i, 1, o - 1) → liste13