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动画演示几何变换与积分

动画演示几何变换与积分
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2017-04-03 09:48
测试改名0积分几何作图
①本范例通过动画演示三角形、椭圆等图形的旋转与变换，并展示积分的上下和计算过程；②涉及核心数学概念包括角度、三角形、统计特征、椭圆、定积分、棱柱、黎曼和；③作图要点运用了 Rotate, Angle, Segment, Ray, Point, LineBisector, Line, OrthogonalLine, Intersect, Dilate, Midpoint, Min, Circle, CircleSector, Polygon 等GeoGebra命令；④适合高中及以上数学学习，用于理解几何变换与微积分概念。

GeoGebra 命令及参数

  1. Rotate(A, (-((a * π / 180))), B) → A'
  2. Angle(A', B, A) → α
  3. Segment(A, B) → f
  4. Ray(B, A') → g
  5. Point(g) → C
  6. Segment(A, C) → h
  7. Segment(B, C) → i
  8. LineBisector(i) → j
  9. LineBisector(f) → k
  10. Line(A, B) → m
  11. OrthogonalLine(C, m) → n
  12. Intersect(m, n) → E
  13. Angle(E, C, A) → γ
  14. Angle(E, A, C) → ε
  15. Dilate(C, If[3 < o ≤ 4, 4 - o, 0], E) → C'_1
  16. Dilate(B, If[3 < o ≤ 4, 4 - o, 0], E) → B'
  17. Midpoint(A, B) → J
  18. Segment(A, E) → g_1
  19. Segment(A, J) → h_1
  20. Min(f, i) → u
  21. Circle(B, (0.2 * u)) → r_1
  22. Intersect(r_1, f) → K,
  23. Intersect(r_1, i) → L,
  24. CircleSector(B, L, K) → s_1
  25. Point(f) → M
  26. Segment(C, M) → p
  27. Line(C, M) → q
  28. OrthogonalLine(A, q) → r
  29. Intersect(q, r) → N
  30. Line(C, B) → s
  31. OrthogonalLine(A, s) → c
  32. Intersect(s, c) → O
  33. Line(N, O) → e
  34. OrthogonalLine(C, e) → i_1
  35. Intersect(e, i_1) → P
  36. Angle(A, C, M) → θ
  37. Angle(O, C, P) → ι
  38. Segment(C, P) → j_1
  39. Min({h, p, i, j_1}) → v
  40. Circle(C, (0.4 * v)) → c_1
  41. Intersect(c_1, h) → Q,
  42. Intersect(c_1, p) → R,
  43. CircleSector(C, Q, R) → d_1
  44. Dilate(C, If[0 < o ≤ 1, 1 - o, 0], M) → C'_2
  45. Segment(C, C'_2) → t
  46. Angle(M, N, A) → κ_1
  47. Dilate(M, If[1 < o ≤ 2, 2 - o, 0], N) → M'
  48. Dilate(A, If[1 < o ≤ 2, 2 - o, 0], N) → A'_1
  49. Segment(M, M') → f_1
  50. Segment(A, A'_1) → k_1
  51. Dilate(A, If[2 < o ≤ 3, 3 - o, 0], O) → A'_2
  52. Segment(A, A'_2) → l_1
  53. Dilate(N, If[3 < o ≤ 4, 4 - o, 0], O) → N'
  54. Segment(N, N') → m_1
  55. Dilate(O, If[4 < o ≤ 5, 5 - o, 0], P) → O'
  56. Dilate(C, If[4 < o ≤ 5, 5 - o, 0], P) → C'_3
  57. Angle(C, P, O) → ζ
  58. Segment(O, O') → n_1
  59. Segment(C, C'_3) → p_1
  60. Rotate(Q, If[5 < o ≤ 6, ((o - 5) * θ), θ], C) → Q'
  61. CircleSector(C, Q, Q') → e_1
  62. Angle(A, C, B) → κ
  63. Polygon(A, B, C) → poly1, c_2, a_1, b
  64. Rotate(d_1, If[6.5 < o ≤ 7.5, ((o - 6.5) * κ), κ], C) → q_1
  65. Circle(B, 1) → d
  66. Circle(C, 1) → t_1
  67. Intersect(d, s) → D, F
  68. Intersect(t_1, s) → G, H
  69. Ray(B, F) → l
  70. Ray(C, G) → b_1
  71. Angle(C, O, A) → β