积极 AI Logo 积极 AI

交互式多边形台球

交互式多边形台球
几何画板及绘图内容加载中，请稍等……
2020-03-12 05:02
多边形向量解析几何几何作图
①本范例演示了在多边形内进行台球运动的轨迹模拟；②涉及的核心数学概念包括几何反射、向量运算、矩阵变换、解析几何等；③作图要点使用了PolyLine、Point、Reflect_Polygon5、Vector等GeoGebra命令与对象；④适合高中及以上学生用于理解几何变换与轨迹问题，也可用于微积分中的积分概念教学。

GeoGebra 命令及参数

  1. PolyLine(A, B, C, D, E, A) → a
  2. Point(a) → Q
  3. PointIn(Polygon[A, B, C, D, E]) → P
  4. Reflect_Polygon5(A, B, C, D, E, A1, A2) → A3
  5. Reflect_Polygon5(A, B, C, D, E, A2, A3) → A4
  6. Reflect_Polygon5(A, B, C, D, E, A3, A4) → A5
  7. Reflect_Polygon5(A, B, C, D, E, A4, A5) → A6
  8. Reflect_Polygon5(A, B, C, D, E, A5, A6) → A7
  9. Reflect_Polygon5(A, B, C, D, E, A6, A7) → A8
  10. Reflect_Polygon5(A, B, C, D, E, A7, A8) → A9
  11. Reflect_Polygon5(A, B, C, D, E, A8, A9) → A10
  12. Reflect_Polygon5(A, B, C, D, E, A9, A10) → A11
  13. Reflect_Polygon5(A, B, C, D, E, A10, A11) → A12
  14. Reflect_Polygon5(A, B, C, D, E, A11, A12) → A13
  15. Reflect_Polygon5(A, B, C, D, E, A12, A13) → A14
  16. Reflect_Polygon5(A, B, C, D, E, A13, A14) → A15
  17. Reflect_Polygon5(A, B, C, D, E, A14, A15) → A16
  18. Reflect_Polygon5(A, B, C, D, E, A15, A16) → A17
  19. Reflect_Polygon5(A, B, C, D, E, A16, A17) → A18
  20. Reflect_Polygon5(A, B, C, D, E, A17, A18) → A19
  21. Reflect_Polygon5(A, B, C, D, E, A18, A19) → A20
  22. Reflect_Polygon5(A, B, C, D, E, A19, A20) → A21
  23. Reflect_Polygon5(A, B, C, D, E, A20, A21) → A22
  24. Reflect_Polygon5(A, B, C, D, E, A21, A22) → A23
  25. Reflect_Polygon5(A, B, C, D, E, A22, A23) → A24
  26. Reflect_Polygon5(A, B, C, D, E, A23, A24) → A25
  27. Reflect_Polygon5(A, B, C, D, E, A24, A25) → A26
  28. Reflect_Polygon5(A, B, C, D, E, A25, A26) → A27
  29. Reflect_Polygon5(A, B, C, D, E, A26, A27) → A28
  30. Reflect_Polygon5(A, B, C, D, E, A27, A28) → A29
  31. Reflect_Polygon5(A, B, C, D, E, A28, A29) → A30
  32. Reflect_Polygon5(A, B, C, D, E, A29, A30) → A31
  33. Reflect_Polygon5(A, B, C, D, E, A30, A31) → A32
  34. Reflect_Polygon5(A, B, C, D, E, A31, A32) → A33
  35. Reflect_Polygon5(A, B, C, D, E, A32, A33) → A34
  36. Reflect_Polygon5(A, B, C, D, E, A33, A34) → A35
  37. Reflect_Polygon5(A, B, C, D, E, A34, A35) → A36
  38. Reflect_Polygon5(A, B, C, D, E, A35, A36) → A37
  39. Reflect_Polygon5(A, B, C, D, E, A36, A37) → A38
  40. Reflect_Polygon5(A, B, C, D, E, A37, A38) → A39
  41. Reflect_Polygon5(A, B, C, D, E, A38, A39) → A40
  42. Reflect_Polygon5(A, B, C, D, E, A39, A40) → A41
  43. Sequence(Cell[1, i], i, 1, n + 1) → list1
  44. PolyLine(list1) → b
  45. Reflect_Polygon5(A, B, C, D, E, A40, A41) → A42
  46. Reflect_Polygon5(A, B, C, D, E, A41, A42) → A43
  47. Reflect_Polygon5(A, B, C, D, E, A42, A43) → A44
  48. Reflect_Polygon5(A, B, C, D, E, A43, A44) → A45
  49. Reflect_Polygon5(A, B, C, D, E, A44, A45) → A46
  50. Reflect_Polygon5(A, B, C, D, E, A45, A46) → A47
  51. Reflect_Polygon5(A, B, C, D, E, A46, A47) → A48
  52. Reflect_Polygon5(A, B, C, D, E, A47, A48) → A49
  53. Reflect_Polygon5(A, B, C, D, E, A48, A49) → A50
  54. Reflect_Polygon5(A, B, C, D, E, A49, A50) → A51
  55. Reflect_Polygon5(A, B, C, D, E, A50, A51) → A52
  56. Reflect_Polygon5(A, B, C, D, E, A51, A52) → A53
  57. Reflect_Polygon5(A, B, C, D, E, A52, A53) → A54
  58. Reflect_Polygon5(A, B, C, D, E, A53, A54) → A55
  59. Reflect_Polygon5(A, B, C, D, E, A54, A55) → A56
  60. Reflect_Polygon5(A, B, C, D, E, A55, A56) → A57
  61. Reflect_Polygon5(A, B, C, D, E, A56, A57) → A58
  62. Reflect_Polygon5(A, B, C, D, E, A57, A58) → A59
  63. Reflect_Polygon5(A, B, C, D, E, A58, A59) → A60
  64. Reflect_Polygon5(A, B, C, D, E, A59, A60) → A61
  65. Vector(Cell[1, floor(n) + 1], Cell[1, floor(n) + 1] + ((n - floor(n)) * (Cell[1, floor(n) + 2] - Cell[1, floor(n) + 1]))) → u
  66. Polygon(A, E, D, C, B) → poly1, a_1, e, d_1, c_1, b_1