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捕食曲线

捕食曲线
几何画板及绘图内容加载中，请稍等……
2019-02-25 17:55
向量数列几何作图
这个范例演示了捕食曲线的形成过程。它涉及向量和几何作图的核心概念。通过使用Sequence和Polygon命令，可以动态地展示多个点的运动轨迹。适合高中数学教学，特别是解析几何和向量课程。

GeoGebra 命令及参数

  1. Sequence(Element[B1, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B1, Mod[i, 5] + 1], Element[B1, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B2
  2. Sequence(Element[B2, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B2, Mod[i, 5] + 1], Element[B2, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B3
  3. Sequence(Element[B3, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B3, Mod[i, 5] + 1], Element[B3, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B4
  4. Sequence(Element[B4, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B4, Mod[i, 5] + 1], Element[B4, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B5
  5. Sequence(Element[B5, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B5, Mod[i, 5] + 1], Element[B5, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B6
  6. Sequence(Element[B6, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B6, Mod[i, 5] + 1], Element[B6, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B7
  7. Sequence(Element[B7, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B7, Mod[i, 5] + 1], Element[B7, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B8
  8. Sequence(Element[B8, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B8, Mod[i, 5] + 1], Element[B8, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B9
  9. Sequence(Element[B9, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B9, Mod[i, 5] + 1], Element[B9, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B10
  10. Sequence(Element[B10, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B10, Mod[i, 5] + 1], Element[B10, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B11
  11. Sequence(Element[B11, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B11, Mod[i, 5] + 1], Element[B11, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B12
  12. Sequence(Element[B12, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B12, Mod[i, 5] + 1], Element[B12, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B13
  13. Sequence(Element[B13, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B13, Mod[i, 5] + 1], Element[B13, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B14
  14. Sequence(Element[B14, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B14, Mod[i, 5] + 1], Element[B14, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B15
  15. Sequence(Element[B15, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B15, Mod[i, 5] + 1], Element[B15, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B16
  16. Sequence(Element[B16, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B16, Mod[i, 5] + 1], Element[B16, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B17
  17. Sequence(Element[B17, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B17, Mod[i, 5] + 1], Element[B17, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B18
  18. Sequence(Element[B18, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B18, Mod[i, 5] + 1], Element[B18, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B19
  19. Sequence(Element[B19, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B19, Mod[i, 5] + 1], Element[B19, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B20
  20. Polygon(B1) → C1
  21. Polygon(B2) → C2
  22. Polygon(B3) → C3
  23. Polygon(B4) → C4
  24. Polygon(B5) → C5
  25. Polygon(B6) → C6
  26. Polygon(B7) → C7
  27. Polygon(B8) → C8
  28. Polygon(B9) → C9
  29. Polygon(B10) → C10
  30. Polygon(B11) → C11
  31. Polygon(B12) → C12
  32. Polygon(B13) → C13
  33. Polygon(B14) → C14
  34. Polygon(B15) → C15
  35. Polygon(B16) → C16
  36. Polygon(B17) → C17
  37. Polygon(B18) → C18
  38. Polygon(B19) → C19
  39. Polygon(B20) → C20
  40. Sequence(Element[B20, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B20, Mod[i, 5] + 1], Element[B20, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B21
  41. Sequence(Element[B21, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B21, Mod[i, 5] + 1], Element[B21, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B22
  42. Sequence(Element[B22, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B22, Mod[i, 5] + 1], Element[B22, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B23
  43. Sequence(Element[B23, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B23, Mod[i, 5] + 1], Element[B23, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B24
  44. Sequence(Element[B24, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B24, Mod[i, 5] + 1], Element[B24, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B25
  45. Sequence(Element[B25, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B25, Mod[i, 5] + 1], Element[B25, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B26
  46. Sequence(Element[B26, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B26, Mod[i, 5] + 1], Element[B26, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B27
  47. Sequence(Element[B27, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B27, Mod[i, 5] + 1], Element[B27, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B28
  48. Sequence(Element[B28, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B28, Mod[i, 5] + 1], Element[B28, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B29
  49. Sequence(Element[B29, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B29, Mod[i, 5] + 1], Element[B29, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B30
  50. Sequence(Element[B30, Mod[i, 5] + 1] + (speed * UnitVector[Vector[Element[B30, Mod[i, 5] + 1], Element[B30, Mod[i + 1, 5] + 1]]]), i, 0, 4) → B31
  51. Polygon(B21) → C21
  52. Polygon(B22) → C22
  53. Polygon(B23) → C23
  54. Polygon(B24) → C24
  55. Polygon(B25) → C25
  56. Polygon(B26) → C26
  57. Polygon(B27) → C27
  58. Polygon(B28) → C28
  59. Polygon(B29) → C29
  60. Polygon(B30) → C30
  61. Polygon(B31) → C31
  62. Sequence(Segment[Element[B2, i], Element[B1, i]], i, 1, 5) → D2
  63. Sequence(Segment[Element[B3, i], Element[B2, i]], i, 1, 5) → D3
  64. Sequence(Segment[Element[B4, i], Element[B3, i]], i, 1, 5) → D4
  65. Sequence(Segment[Element[B5, i], Element[B4, i]], i, 1, 5) → D5
  66. Sequence(Segment[Element[B6, i], Element[B5, i]], i, 1, 5) → D6
  67. Sequence(Segment[Element[B7, i], Element[B6, i]], i, 1, 5) → D7
  68. Sequence(Segment[Element[B8, i], Element[B7, i]], i, 1, 5) → D8
  69. Sequence(Segment[Element[B9, i], Element[B8, i]], i, 1, 5) → D9
  70. Sequence(Segment[Element[B10, i], Element[B9, i]], i, 1, 5) → D10
  71. Sequence(Segment[Element[B11, i], Element[B10, i]], i, 1, 5) → D11
  72. Sequence(Segment[Element[B12, i], Element[B11, i]], i, 1, 5) → D12
  73. Sequence(Segment[Element[B13, i], Element[B12, i]], i, 1, 5) → D13
  74. Sequence(Segment[Element[B14, i], Element[B13, i]], i, 1, 5) → D14
  75. Sequence(Segment[Element[B15, i], Element[B14, i]], i, 1, 5) → D15
  76. Sequence(Segment[Element[B16, i], Element[B15, i]], i, 1, 5) → D16
  77. Sequence(Segment[Element[B17, i], Element[B16, i]], i, 1, 5) → D17
  78. Sequence(Segment[Element[B18, i], Element[B17, i]], i, 1, 5) → D18
  79. Sequence(Segment[Element[B19, i], Element[B18, i]], i, 1, 5) → D19
  80. Sequence(Segment[Element[B20, i], Element[B19, i]], i, 1, 5) → D20
  81. Sequence(Segment[Element[B21, i], Element[B20, i]], i, 1, 5) → D21
  82. Sequence(Segment[Element[B22, i], Element[B21, i]], i, 1, 5) → D22
  83. Sequence(Segment[Element[B23, i], Element[B22, i]], i, 1, 5) → D23
  84. Sequence(Segment[Element[B24, i], Element[B23, i]], i, 1, 5) → D24
  85. Sequence(Segment[Element[B25, i], Element[B24, i]], i, 1, 5) → D25
  86. Sequence(Segment[Element[B26, i], Element[B25, i]], i, 1, 5) → D26
  87. Sequence(Segment[Element[B27, i], Element[B26, i]], i, 1, 5) → D27
  88. Sequence(Segment[Element[B28, i], Element[B27, i]], i, 1, 5) → D28
  89. Sequence(Segment[Element[B29, i], Element[B28, i]], i, 1, 5) → D29
  90. Sequence(Segment[Element[B30, i], Element[B29, i]], i, 1, 5) → D30
  91. Sequence(Segment[Element[B31, i], Element[B30, i]], i, 1, 5) → D31