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复参数曲线

复参数曲线
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2019-07-24 14:00
函数复数参数方程
这个范例展示了复参数曲线的绘制方法。它涉及复数和参数方程的核心数学概念。通过使用GeoGebra命令如CurveCartesian、Sequence和Element，可以动态地绘制复参数曲线。适合高中数学教学和学习。

GeoGebra 命令及参数

  1. CurveCartesian(t, Im(t), Re(t), t, a, b) → curve
  2. Sequence(Segment[(i, 0, 0), curve(i)], i, a, b, eps) → Segmts
  3. Element(listvectordirection, faces) → Selectedvector
  4. Segment((a + ((b - a) * 1 / n), 0, 0), curve(a + ((b - a) * 1 / n))) → A1
  5. Segment((a + ((b - a) * 2 / n), 0, 0), curve(a + ((b - a) * 2 / n))) → A2
  6. Segment((a + ((b - a) * 3 / n), 0, 0), curve(a + ((b - a) * 3 / n))) → A3
  7. Segment((a + ((b - a) * 4 / n), 0, 0), curve(a + ((b - a) * 4 / n))) → A4
  8. Segment((a + ((b - a) * 5 / n), 0, 0), curve(a + ((b - a) * 5 / n))) → A5
  9. Segment((a + ((b - a) * 6 / n), 0, 0), curve(a + ((b - a) * 6 / n))) → A6
  10. Segment((a + ((b - a) * 7 / n), 0, 0), curve(a + ((b - a) * 7 / n))) → A7
  11. Segment((a + ((b - a) * 8 / n), 0, 0), curve(a + ((b - a) * 8 / n))) → A8
  12. Segment((a + ((b - a) * 9 / n), 0, 0), curve(a + ((b - a) * 9 / n))) → A9
  13. Segment((a + ((b - a) * 10 / n), 0, 0), curve(a + ((b - a) * 10 / n))) → A10
  14. Segment((a + ((b - a) * 11 / n), 0, 0), curve(a + ((b - a) * 11 / n))) → A11
  15. Segment((a + ((b - a) * 12 / n), 0, 0), curve(a + ((b - a) * 12 / n))) → A12
  16. Segment((a + ((b - a) * 13 / n), 0, 0), curve(a + ((b - a) * 13 / n))) → A13
  17. Segment((a + ((b - a) * 14 / n), 0, 0), curve(a + ((b - a) * 14 / n))) → A14
  18. Segment((a + ((b - a) * 15 / n), 0, 0), curve(a + ((b - a) * 15 / n))) → A15
  19. Segment((a + ((b - a) * 16 / n), 0, 0), curve(a + ((b - a) * 16 / n))) → A16
  20. Segment((a + ((b - a) * 17 / n), 0, 0), curve(a + ((b - a) * 17 / n))) → A17
  21. Segment((a + ((b - a) * 18 / n), 0, 0), curve(a + ((b - a) * 18 / n))) → A18
  22. Segment((a + ((b - a) * 19 / n), 0, 0), curve(a + ((b - a) * 19 / n))) → A19
  23. Segment((a + ((b - a) * 20 / n), 0, 0), curve(a + ((b - a) * 20 / n))) → A20
  24. Segment((a + ((b - a) * 21 / n), 0, 0), curve(a + ((b - a) * 21 / n))) → A21
  25. Segment((a + ((b - a) * 22 / n), 0, 0), curve(a + ((b - a) * 22 / n))) → A22
  26. Segment((a + ((b - a) * 23 / n), 0, 0), curve(a + ((b - a) * 23 / n))) → A23
  27. Segment((a + ((b - a) * 24 / n), 0, 0), curve(a + ((b - a) * 24 / n))) → A24
  28. Segment((a + ((b - a) * 25 / n), 0, 0), curve(a + ((b - a) * 25 / n))) → A25
  29. Segment((a + ((b - a) * 26 / n), 0, 0), curve(a + ((b - a) * 26 / n))) → A26
  30. Segment((a + ((b - a) * 27 / n), 0, 0), curve(a + ((b - a) * 27 / n))) → A27
  31. Segment((a + ((b - a) * 28 / n), 0, 0), curve(a + ((b - a) * 28 / n))) → A28
  32. Segment((a + ((b - a) * 29 / n), 0, 0), curve(a + ((b - a) * 29 / n))) → A29
  33. Segment((a + ((b - a) * 30 / n), 0, 0), curve(a + ((b - a) * 30 / n))) → A30
  34. Segment((a + ((b - a) * 31 / n), 0, 0), curve(a + ((b - a) * 31 / n))) → A31
  35. Segment((a + ((b - a) * 32 / n), 0, 0), curve(a + ((b - a) * 32 / n))) → A32
  36. Segment((a + ((b - a) * 33 / n), 0, 0), curve(a + ((b - a) * 33 / n))) → A33
  37. Segment((a + ((b - a) * 34 / n), 0, 0), curve(a + ((b - a) * 34 / n))) → A34
  38. Segment((a + ((b - a) * 35 / n), 0, 0), curve(a + ((b - a) * 35 / n))) → A35
  39. Segment((a + ((b - a) * 36 / n), 0, 0), curve(a + ((b - a) * 36 / n))) → A36
  40. Segment((a + ((b - a) * 37 / n), 0, 0), curve(a + ((b - a) * 37 / n))) → A37
  41. Segment((a + ((b - a) * 38 / n), 0, 0), curve(a + ((b - a) * 38 / n))) → A38
  42. Segment((a + ((b - a) * 39 / n), 0, 0), curve(a + ((b - a) * 39 / n))) → A39
  43. Segment((a + ((b - a) * 40 / n), 0, 0), curve(a + ((b - a) * 40 / n))) → A40
  44. Segment((a + ((b - a) * 41 / n), 0, 0), curve(a + ((b - a) * 41 / n))) → A41
  45. Segment((a + ((b - a) * 42 / n), 0, 0), curve(a + ((b - a) * 42 / n))) → A42
  46. Segment((a + ((b - a) * 43 / n), 0, 0), curve(a + ((b - a) * 43 / n))) → A43
  47. Segment((a + ((b - a) * 44 / n), 0, 0), curve(a + ((b - a) * 44 / n))) → A44
  48. Segment((a + ((b - a) * 45 / n), 0, 0), curve(a + ((b - a) * 45 / n))) → A45
  49. Segment((a + ((b - a) * 46 / n), 0, 0), curve(a + ((b - a) * 46 / n))) → A46
  50. Segment((a + ((b - a) * 47 / n), 0, 0), curve(a + ((b - a) * 47 / n))) → A47
  51. Segment((a + ((b - a) * 48 / n), 0, 0), curve(a + ((b - a) * 48 / n))) → A48
  52. Segment((a + ((b - a) * 49 / n), 0, 0), curve(a + ((b - a) * 49 / n))) → A49
  53. Segment((a + ((b - a) * 50 / n), 0, 0), curve(a + ((b - a) * 50 / n))) → A50
  54. Segment((a + ((b - a) * 51 / n), 0, 0), curve(a + ((b - a) * 51 / n))) → A51
  55. Segment((a + ((b - a) * 52 / n), 0, 0), curve(a + ((b - a) * 52 / n))) → A52
  56. Segment((a + ((b - a) * 53 / n), 0, 0), curve(a + ((b - a) * 53 / n))) → A53
  57. Segment((a + ((b - a) * 54 / n), 0, 0), curve(a + ((b - a) * 54 / n))) → A54
  58. Segment((a + ((b - a) * 55 / n), 0, 0), curve(a + ((b - a) * 55 / n))) → A55
  59. Segment((a + ((b - a) * 56 / n), 0, 0), curve(a + ((b - a) * 56 / n))) → A56
  60. Segment((a + ((b - a) * 57 / n), 0, 0), curve(a + ((b - a) * 57 / n))) → A57
  61. Segment((a + ((b - a) * 58 / n), 0, 0), curve(a + ((b - a) * 58 / n))) → A58
  62. Segment((a + ((b - a) * 59 / n), 0, 0), curve(a + ((b - a) * 59 / n))) → A59
  63. Segment((a + ((b - a) * 60 / n), 0, 0), curve(a + ((b - a) * 60 / n))) → A60
  64. Segment((a + ((b - a) * 61 / n), 0, 0), curve(a + ((b - a) * 61 / n))) → A61
  65. Segment((a + ((b - a) * 62 / n), 0, 0), curve(a + ((b - a) * 62 / n))) → A62
  66. Segment((a + ((b - a) * 63 / n), 0, 0), curve(a + ((b - a) * 63 / n))) → A63
  67. Segment((a + ((b - a) * 64 / n), 0, 0), curve(a + ((b - a) * 64 / n))) → A64
  68. Segment((a + ((b - a) * 65 / n), 0, 0), curve(a + ((b - a) * 65 / n))) → A65
  69. Segment((a + ((b - a) * 66 / n), 0, 0), curve(a + ((b - a) * 66 / n))) → A66
  70. Segment((a + ((b - a) * 67 / n), 0, 0), curve(a + ((b - a) * 67 / n))) → A67
  71. Segment((a + ((b - a) * 68 / n), 0, 0), curve(a + ((b - a) * 68 / n))) → A68
  72. Segment((a + ((b - a) * 69 / n), 0, 0), curve(a + ((b - a) * 69 / n))) → A69
  73. Segment((a + ((b - a) * 70 / n), 0, 0), curve(a + ((b - a) * 70 / n))) → A70
  74. Segment((a + ((b - a) * 71 / n), 0, 0), curve(a + ((b - a) * 71 / n))) → A71
  75. Segment((a + ((b - a) * 72 / n), 0, 0), curve(a + ((b - a) * 72 / n))) → A72
  76. Segment((a + ((b - a) * 73 / n), 0, 0), curve(a + ((b - a) * 73 / n))) → A73
  77. Segment((a + ((b - a) * 74 / n), 0, 0), curve(a + ((b - a) * 74 / n))) → A74
  78. Segment((a + ((b - a) * 75 / n), 0, 0), curve(a + ((b - a) * 75 / n))) → A75
  79. Segment((a + ((b - a) * 76 / n), 0, 0), curve(a + ((b - a) * 76 / n))) → A76
  80. Segment((a + ((b - a) * 77 / n), 0, 0), curve(a + ((b - a) * 77 / n))) → A77
  81. Segment((a + ((b - a) * 78 / n), 0, 0), curve(a + ((b - a) * 78 / n))) → A78
  82. Segment((a + ((b - a) * 79 / n), 0, 0), curve(a + ((b - a) * 79 / n))) → A79
  83. Segment((a + ((b - a) * 80 / n), 0, 0), curve(a + ((b - a) * 80 / n))) → A80
  84. Segment((a + ((b - a) * 81 / n), 0, 0), curve(a + ((b - a) * 81 / n))) → A81
  85. Segment((a + ((b - a) * 82 / n), 0, 0), curve(a + ((b - a) * 82 / n))) → A82
  86. Segment((a + ((b - a) * 83 / n), 0, 0), curve(a + ((b - a) * 83 / n))) → A83
  87. Segment((a + ((b - a) * 84 / n), 0, 0), curve(a + ((b - a) * 84 / n))) → A84
  88. Segment((a + ((b - a) * 85 / n), 0, 0), curve(a + ((b - a) * 85 / n))) → A85
  89. Segment((a + ((b - a) * 86 / n), 0, 0), curve(a + ((b - a) * 86 / n))) → A86
  90. Segment((a + ((b - a) * 87 / n), 0, 0), curve(a + ((b - a) * 87 / n))) → A87
  91. Segment((a + ((b - a) * 88 / n), 0, 0), curve(a + ((b - a) * 88 / n))) → A88
  92. Segment((a + ((b - a) * 89 / n), 0, 0), curve(a + ((b - a) * 89 / n))) → A89
  93. Segment((a + ((b - a) * 90 / n), 0, 0), curve(a + ((b - a) * 90 / n))) → A90
  94. Segment((a + ((b - a) * 91 / n), 0, 0), curve(a + ((b - a) * 91 / n))) → A91
  95. Segment((a + ((b - a) * 92 / n), 0, 0), curve(a + ((b - a) * 92 / n))) → A92
  96. Segment((a + ((b - a) * 93 / n), 0, 0), curve(a + ((b - a) * 93 / n))) → A93
  97. Segment((a + ((b - a) * 94 / n), 0, 0), curve(a + ((b - a) * 94 / n))) → A94
  98. Segment((a + ((b - a) * 95 / n), 0, 0), curve(a + ((b - a) * 95 / n))) → A95
  99. Segment((a + ((b - a) * 96 / n), 0, 0), curve(a + ((b - a) * 96 / n))) → A96
  100. Segment((a + ((b - a) * 97 / n), 0, 0), curve(a + ((b - a) * 97 / n))) → A97
  101. Segment((a + ((b - a) * 98 / n), 0, 0), curve(a + ((b - a) * 98 / n))) → A98
  102. Segment((a + ((b - a) * 99 / n), 0, 0), curve(a + ((b - a) * 99 / n))) → A99
  103. Segment((a + ((b - a) * 100 / n), 0, 0), curve(a + ((b - a) * 100 / n))) → A100
  104. Segment((a + ((b - a) * 101 / n), 0, 0), curve(a + ((b - a) * 101 / n))) → A101
  105. Segment((a + ((b - a) * 102 / n), 0, 0), curve(a + ((b - a) * 102 / n))) → A102
  106. Segment((a + ((b - a) * 103 / n), 0, 0), curve(a + ((b - a) * 103 / n))) → A103
  107. Segment((a + ((b - a) * 104 / n), 0, 0), curve(a + ((b - a) * 104 / n))) → A104
  108. Segment((a + ((b - a) * 105 / n), 0, 0), curve(a + ((b - a) * 105 / n))) → A105
  109. Segment((a + ((b - a) * 106 / n), 0, 0), curve(a + ((b - a) * 106 / n))) → A106
  110. Segment((a + ((b - a) * 107 / n), 0, 0), curve(a + ((b - a) * 107 / n))) → A107
  111. Segment((a + ((b - a) * 108 / n), 0, 0), curve(a + ((b - a) * 108 / n))) → A108
  112. Segment((a + ((b - a) * 109 / n), 0, 0), curve(a + ((b - a) * 109 / n))) → A109
  113. Segment((a + ((b - a) * 110 / n), 0, 0), curve(a + ((b - a) * 110 / n))) → A110
  114. Segment((a + ((b - a) * 111 / n), 0, 0), curve(a + ((b - a) * 111 / n))) → A111
  115. Segment((a + ((b - a) * 112 / n), 0, 0), curve(a + ((b - a) * 112 / n))) → A112
  116. Segment((a + ((b - a) * 113 / n), 0, 0), curve(a + ((b - a) * 113 / n))) → A113
  117. Segment((a + ((b - a) * 114 / n), 0, 0), curve(a + ((b - a) * 114 / n))) → A114
  118. Segment((a + ((b - a) * 115 / n), 0, 0), curve(a + ((b - a) * 115 / n))) → A115
  119. Segment((a + ((b - a) * 116 / n), 0, 0), curve(a + ((b - a) * 116 / n))) → A116
  120. Segment((a + ((b - a) * 117 / n), 0, 0), curve(a + ((b - a) * 117 / n))) → A117
  121. Segment((a + ((b - a) * 118 / n), 0, 0), curve(a + ((b - a) * 118 / n))) → A118
  122. Segment((a + ((b - a) * 119 / n), 0, 0), curve(a + ((b - a) * 119 / n))) → A119
  123. Segment((a + ((b - a) * 120 / n), 0, 0), curve(a + ((b - a) * 120 / n))) → A120
  124. Segment((a + ((b - a) * 121 / n), 0, 0), curve(a + ((b - a) * 121 / n))) → A121
  125. Segment((a + ((b - a) * 122 / n), 0, 0), curve(a + ((b - a) * 122 / n))) → A122
  126. Segment((a + ((b - a) * 123 / n), 0, 0), curve(a + ((b - a) * 123 / n))) → A123
  127. Segment((a + ((b - a) * 124 / n), 0, 0), curve(a + ((b - a) * 124 / n))) → A124
  128. Segment((a + ((b - a) * 125 / n), 0, 0), curve(a + ((b - a) * 125 / n))) → A125
  129. Segment((a + ((b - a) * 126 / n), 0, 0), curve(a + ((b - a) * 126 / n))) → A126
  130. Segment((a + ((b - a) * 127 / n), 0, 0), curve(a + ((b - a) * 127 / n))) → A127
  131. Segment((a + ((b - a) * 128 / n), 0, 0), curve(a + ((b - a) * 128 / n))) → A128
  132. Segment((a + ((b - a) * 129 / n), 0, 0), curve(a + ((b - a) * 129 / n))) → A129
  133. Segment((a + ((b - a) * 130 / n), 0, 0), curve(a + ((b - a) * 130 / n))) → A130
  134. Segment((a + ((b - a) * 131 / n), 0, 0), curve(a + ((b - a) * 131 / n))) → A131
  135. Segment((a + ((b - a) * 132 / n), 0, 0), curve(a + ((b - a) * 132 / n))) → A132
  136. Segment((a + ((b - a) * 133 / n), 0, 0), curve(a + ((b - a) * 133 / n))) → A133
  137. Segment((a + ((b - a) * 134 / n), 0, 0), curve(a + ((b - a) * 134 / n))) → A134
  138. Segment((a + ((b - a) * 135 / n), 0, 0), curve(a + ((b - a) * 135 / n))) → A135
  139. Segment((a + ((b - a) * 136 / n), 0, 0), curve(a + ((b - a) * 136 / n))) → A136
  140. Segment((a + ((b - a) * 137 / n), 0, 0), curve(a + ((b - a) * 137 / n))) → A137
  141. Segment((a + ((b - a) * 138 / n), 0, 0), curve(a + ((b - a) * 138 / n))) → A138
  142. Segment((a + ((b - a) * 139 / n), 0, 0), curve(a + ((b - a) * 139 / n))) → A139
  143. Segment((a + ((b - a) * 140 / n), 0, 0), curve(a + ((b - a) * 140 / n))) → A140
  144. Segment((a + ((b - a) * 141 / n), 0, 0), curve(a + ((b - a) * 141 / n))) → A141
  145. Segment((a + ((b - a) * 142 / n), 0, 0), curve(a + ((b - a) * 142 / n))) → A142
  146. Segment((a + ((b - a) * 143 / n), 0, 0), curve(a + ((b - a) * 143 / n))) → A143
  147. Segment((a + ((b - a) * 144 / n), 0, 0), curve(a + ((b - a) * 144 / n))) → A144
  148. Segment((a + ((b - a) * 145 / n), 0, 0), curve(a + ((b - a) * 145 / n))) → A145
  149. Segment((a + ((b - a) * 146 / n), 0, 0), curve(a + ((b - a) * 146 / n))) → A146
  150. Segment((a + ((b - a) * 147 / n), 0, 0), curve(a + ((b - a) * 147 / n))) → A147
  151. Segment((a + ((b - a) * 148 / n), 0, 0), curve(a + ((b - a) * 148 / n))) → A148
  152. Segment((a + ((b - a) * 149 / n), 0, 0), curve(a + ((b - a) * 149 / n))) → A149
  153. Segment((a + ((b - a) * 150 / n), 0, 0), curve(a + ((b - a) * 150 / n))) → A150
  154. Textfield(f) → InputBox1