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动态几何图形演示 by Tim Brzezinski (12)

动态几何图形演示 by Tim Brzezinski (12)
几何画板及绘图内容加载中，请稍等……
2017-12-10 11:39
向量解析几何微积分几何作图
①本范例动态演示了由 Antonio Gutierrez 在 Twitter 上提出的问题，通过可调节的图形展示几何与算术的结合；②涉及核心数学概念包括平面、饼图、几何作图、算术运算、上下和或黎曼和；③作图要点：运用了 Point, Semicircle, Segment, Angle, Rotate, Ray, Intersect, Distance, Polygon, Midpoint, Circle, Dilate, CircleSector, Line, Vector, Translate 等GeoGebra命令；④适合高中及以上学生及数学爱好者用于理解几何变换与积分概念。

GeoGebra 命令及参数

  1. Point(xAxis) → A
  2. Point(xAxis) → B
  3. Semicircle(A, B) → c
  4. Point(c) → C
  5. Segment(A, C) → f
  6. Segment(C, B) → g
  7. Segment(B, A) → h
  8. Angle(B, A, C) → α
  9. Rotate(B, (2 * α / 3), A) → B'
  10. Angle(B, A, B') → β
  11. Ray(A, B') → i
  12. Intersect(g, i) → D
  13. Angle(C, B, A) → γ
  14. Rotate(A, γ, D) → A'
  15. Angle(A, D, A') → δ
  16. Ray(D, A') → j
  17. Intersect(h, xAxis) → E
  18. Intersect(h, j) → F
  19. Distance(D, F) → distanceDF
  20. Distance(D, C) → distanceDC
  21. Segment(A, D) → k
  22. Segment(D, F) → l
  23. Polygon(A, C, B) → t1, b, a, c_1
  24. Rotate(B, β / 2, A) → B'_1
  25. Angle(B, A, B'_1) → ε
  26. Ray(A, B'_1) → m
  27. Intersect(g, m) → G
  28. Segment(A, G) → n
  29. Intersect(l, n) → H
  30. Midpoint(A, H) → I
  31. Segment(A, I) → p
  32. Midpoint(l) → J
  33. Circle(A, (0.5 * p)) → d
  34. Circle(B, (0.25 * l)) → q
  35. Angle(A, C, B) → ζ
  36. Intersect(d, h) → K,
  37. Intersect(d, p) → L,
  38. Dilate(A, If[0 < o ≤ 1, 1 - o, 0], I) → A'_1
  39. Segment(A, A'_1) → r
  40. Dilate(A, If[1 < o ≤ 2, 2 - o, 0], D) → A'_2
  41. Segment(A, A'_2) → s
  42. Dilate(F, If[1 < o ≤ 2, 2 - o, 0], J) → F'
  43. Segment(F, F') → t
  44. Dilate(J, If[2 < o ≤ 3, 3 - o, 0], D) → J'
  45. Segment(J, J') → f_1
  46. Dilate(D, If[3 < o ≤ 4, 4 - o, 0], C) → D'
  47. Dilate(D, If[3 < o ≤ 4, 4 - o, 0], B) → D'_1
  48. Segment(D, D') → g_1
  49. Segment(D, D'_1) → h_1
  50. Intersect(q, g) → M,
  51. Intersect(q, h) → N,
  52. Rotate(K, If[4 < o ≤ 5, ((o - 4) * ε), ε], A) → K'
  53. CircleSector(A, K, K') → d_1
  54. Rotate(d_1, If[6 < o ≤ 7, ((o - 6) * ε), ε], A) → e_1
  55. Rotate(e_1, If[8 < o ≤ 9, ((o - 8) * ε), ε], A) → k_1
  56. Rotate(M, If[11 < o ≤ 12, ((o - 10) * δ), δ], B) → M'
  57. Rotate(M, If[10 < o ≤ 11, ((o - 10) * δ), δ], B) → M'_1
  58. CircleSector(B, M, M'_1) → p_1
  59. Midpoint(D, B) → O
  60. Line(B, f_1) → i_1
  61. Circle(B, 1) → q_1
  62. Intersect(q_1, i_1, 1) → P
  63. Angle(A, B, P) → κ
  64. Dilate(B, If[11 < o ≤ 12, 12 - o, 0], O) → B'_2
  65. Vector(B, B'_2) → u
  66. Translate(p_1, u) → e
  67. Rotate(e, If[12 < o ≤ 13, ((o - 12) * κ), κ], O) → e'
  68. Dilate(O, If[13 < o ≤ 14, 14 - o, 0], D) → O'
  69. Vector(O, O') → v
  70. Translate(e', v) → e''
  71. Angle(C, D, F) → λ
  72. Rotate(D, If[15 < o ≤ 16, ((o - 15) * λ), λ], D) → D'_2
  73. Rotate(D', If[15 < o ≤ 16, ((o - 15) * λ), λ], D) → D''
  74. Segment(D'_2, D'') → j_1
  75. Dilate(D, If[16 < o ≤ 17, 17 - o, 0], J) → D'_3
  76. Vector(D, D'_3) → w
  77. Translate(D, w) → D'_4
  78. Translate(D', w) → D''_1
  79. Segment(D'_4, D''_1) → l_1
  80. Rotate(D'_4, If[17 < o ≤ 18, ((o - 17) * λ), λ], J) → Q
  81. Rotate(D''_1, If[17 < o ≤ 18, ((o - 17) * λ), λ], J) → R
  82. Segment(Q, R) → m_1