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体积变换演示

体积变换演示
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2014-01-24 01:25
立体几何微积分变换几何作图
①本范例通过滑块动态构建几何体，直观演示体积变化过程；②涉及核心数学概念：体积、相似变换、算术平均、定积分、勾股定理；③作图要点：运用Polygon、Dilate、Ray、Translate、Vector、Circle、Segment、Line、Intersect、OrthogonalLine、Semicircle、PointIn等命令及对象；④适合高中阶段数学教学，用于引入体积概念及相似变换应用。

GeoGebra 命令及参数

  1. Polygon(C, D, B) → poly1, b, c, d
  2. Dilate(C, a, A) → C'_1
  3. Dilate(D, a, A) → D'_1
  4. Dilate(B, a, A) → B'_1
  5. Polygon(C'_1, D'_1, B'_1) → poly1'_1, b', c', d'
  6. Ray(A, C) → e
  7. Ray(A, B) → f
  8. Ray(A, D) → g
  9. Translate(C, Vector[(horz, vert)]) → C'_2
  10. Translate(D, Vector[(horz, vert)]) → D'_2
  11. Translate(B, Vector[(horz, vert)]) → B'_2
  12. Polygon(C'_2, D'_2, B'_2) → poly1'_2, b'_1, c'_1, d'_1
  13. Vector(C, C'_2) → u
  14. Vector(B, B'_2) → v
  15. Vector(D, D'_2) → w
  16. Polygon(E, G, 5) → poly2, h, i, j, l, m, I, J, K
  17. Circle(L, M) → p_2
  18. Segment(N, O) → n
  19. Vector(N, O) → z
  20. Translate(p_2, z) → p'
  21. Line(M, L) → q
  22. Intersect(p_2, q, 2) → P
  23. OrthogonalLine(P, q) → r
  24. OrthogonalLine(M, q) → s
  25. OrthogonalLine(L, q) → a_1
  26. Intersect(p', r, 1) → Q
  27. Intersect(p', s, 1) → R
  28. Line(Q, R) → b_1
  29. Intersect(a_1, b_1) → S
  30. Segment(Q, P) → c_1
  31. Segment(R, M) → d_1
  32. Segment(Q, P) → e_1
  33. Segment(R, M) → f_1
  34. Polygon(Q, P, M, R) → poly3, q_1, p_1, m_1, r_1
  35. Semicircle(Q, R) → g_1
  36. Semicircle(M, P) → h_1
  37. Line(K, I) → p
  38. Line(G, E) → i_1
  39. Line(J, p) → j_1
  40. Vector(T, V) → u_1
  41. Translate(poly2, u_1) → poly2'
  42. PointIn(poly2') → U
  43. PointIn(poly2') → W
  44. PointIn(poly2') → Z
  45. PointIn(poly2') → A_1
  46. PointIn(poly2') → B_1
  47. Segment(B_1, K) → k_1
  48. Segment(U, E) → l_1
  49. Segment(W, G) → n_1
  50. Segment(Z, I) → s_1
  51. Segment(A_1, J) → t_1
  52. Segment(B_1, K) → a_2
  53. Segment(U, E) → b_2
  54. Segment(W, G) → c_2
  55. Segment(Z, I) → d_2
  56. Segment(U, W) → e_2
  57. Segment(W, Z) → f_2
  58. Segment(A_1, Z) → g_2
  59. Segment(A_1, B_1) → h_2
  60. Segment(B_1, U) → i_2
  61. Segment(K, J) → j_2
  62. Segment(J, I) → k_2
  63. Segment(I, G) → l_2
  64. Segment(E, G) → m_2
  65. Segment(K, E) → n_2
  66. Vector(C_1, D_1) → v_1
  67. Translate(C, v_1) → C'
  68. Translate(D, v_1) → D'
  69. Translate(B, v_1) → B'
  70. Polygon(C', D', B') → poly1', b'_2, c'_2, d'_2
  71. Segment(E_1, C') → q_2
  72. Segment(B', F_1) → r_2
  73. Segment(D', D) → s_2
  74. Segment(E_1, F_1) → a_3
  75. Segment(C', D') → c_3
  76. Segment(D', B') → d_3
  77. Segment(B', C') → e_3
  78. Segment(E_1, D) → t_2
  79. Segment(D, F_1) → b_3