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Curve of Pursuit

Curve of Pursuit
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2019-02-25 17:55
VectorSequenceGeometric Construction
This example demonstrates the formation of a pursuit curve. It involves core concepts of vectors and geometric construction. Using the Sequence and Polygon commands, it dynamically shows the movement trajectories of multiple points. Suitable for high school mathematics education, particularly in coordinate geometry and vector courses.

GeoGebra Commands & Parameters

  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