积极 AI Logo 积极 AI

彩虹圆与变换：探索几何中的对称与旋转

彩虹圆与变换：探索几何中的对称与旋转
几何画板及绘图内容加载中，请稍等……
2021-07-15 16:56
圆变换几何作图
这个范例展示了如何通过变换生成彩虹圆的几何图形。核心数学概念包括旋转、相似变换和三角函数。作图要点涉及使用GeoGebra命令如Circle, Flatten, Element来创建圆，并利用变换工具调整图形。适合高中生或数学爱好者用于理解几何变换和函数图像的动态变化。

GeoGebra 命令及参数

  1. Circle((-4, 4), 1) → c
  2. Flatten(Zip[Rotate[Zip[Dilate[Rotate[c, (li * (360°) / ((n * b))), C], a^(li), C], li, Li], (k * (360°) / n), C], k, Lk]) → F
  3. Flatten(Zip[Zip["circle" + (k) + (li), k, Lk], li, Li + 1]) → Lname
  4. Element(F, 1) → circle11
  5. Element(F, 2) → circle21
  6. Element(F, 3) → circle31
  7. Element(F, 4) → circle41
  8. Element(F, 5) → circle51
  9. Element(F, 6) → circle61
  10. Element(F, 7) → circle71
  11. Element(F, 8) → circle81
  12. Element(F, 9) → circle91
  13. Element(F, 10) → circle101
  14. Element(F, 11) → circle12
  15. Element(F, 12) → circle22
  16. Element(F, 13) → circle32
  17. Element(F, 14) → circle42
  18. Element(F, 15) → circle52
  19. Element(F, 16) → circle62
  20. Element(F, 17) → circle72
  21. Element(F, 18) → circle82
  22. Element(F, 19) → circle92
  23. Element(F, 20) → circle102
  24. Element(F, 21) → circle13
  25. Element(F, 22) → circle23
  26. Element(F, 23) → circle33
  27. Element(F, 24) → circle43
  28. Element(F, 25) → circle53
  29. Element(F, 26) → circle63
  30. Element(F, 27) → circle73
  31. Element(F, 28) → circle83
  32. Element(F, 29) → circle93
  33. Element(F, 30) → circle103
  34. Element(F, 31) → circle14
  35. Element(F, 32) → circle24
  36. Element(F, 33) → circle34
  37. Element(F, 34) → circle44
  38. Element(F, 35) → circle54
  39. Element(F, 36) → circle64
  40. Element(F, 37) → circle74
  41. Element(F, 38) → circle84
  42. Element(F, 39) → circle94
  43. Element(F, 40) → circle104
  44. Element(F, 41) → circle15
  45. Element(F, 42) → circle25
  46. Element(F, 43) → circle35
  47. Element(F, 44) → circle45
  48. Element(F, 45) → circle55
  49. Element(F, 46) → circle65
  50. Element(F, 47) → circle75
  51. Element(F, 48) → circle85
  52. Element(F, 49) → circle95
  53. Element(F, 50) → circle105
  54. Element(F, 51) → circle16
  55. Element(F, 52) → circle26
  56. Element(F, 53) → circle36
  57. Element(F, 54) → circle46
  58. Element(F, 55) → circle56
  59. Element(F, 56) → circle66
  60. Element(F, 57) → circle76
  61. Element(F, 58) → circle86
  62. Element(F, 59) → circle96
  63. Element(F, 60) → circle106
  64. Element(F, 61) → circle17
  65. Element(F, 62) → circle27
  66. Element(F, 63) → circle37
  67. Element(F, 64) → circle47
  68. Element(F, 65) → circle57
  69. Element(F, 66) → circle67
  70. Element(F, 67) → circle77
  71. Element(F, 68) → circle87
  72. Element(F, 69) → circle97
  73. Element(F, 70) → circle107
  74. Element(F, 71) → circle18
  75. Element(F, 72) → circle28
  76. Element(F, 73) → circle38
  77. Element(F, 74) → circle48
  78. Element(F, 75) → circle58
  79. Element(F, 76) → circle68
  80. Element(F, 77) → circle78
  81. Element(F, 78) → circle88
  82. Element(F, 79) → circle98
  83. Element(F, 80) → circle108
  84. Element(F, 81) → circle19
  85. Element(F, 82) → circle29
  86. Element(F, 83) → circle39
  87. Element(F, 84) → circle49
  88. Element(F, 85) → circle59
  89. Element(F, 86) → circle69
  90. Element(F, 87) → circle79
  91. Element(F, 88) → circle89
  92. Element(F, 89) → circle99
  93. Element(F, 90) → circle109
  94. Element(F, 91) → circle110
  95. Element(F, 92) → circle210
  96. Element(F, 93) → circle310
  97. Element(F, 94) → circle410
  98. Element(F, 95) → circle510
  99. Element(F, 96) → circle610
  100. Element(F, 97) → circle710
  101. Element(F, 98) → circle810
  102. Element(F, 99) → circle910
  103. Element(F, 100) → circle1010
  104. Element(F, 101) → circle111
  105. Element(F, 102) → circle211
  106. Element(F, 103) → circle311
  107. Element(F, 104) → circle411
  108. Element(F, 105) → circle511
  109. Element(F, 106) → circle611
  110. Element(F, 107) → circle711
  111. Element(F, 108) → circle811
  112. Element(F, 109) → circle911
  113. Element(F, 110) → circle1011

AI 绘图提示语参考

绘制一个以点(-4, 4)为中心，半径为1的圆，然后围绕该圆进行旋转和平移变换，生成一系列彩色的同心圆，形成彩虹效果。首先创建一个基础圆，然后通过旋转、缩放和移动操作，生成多个同心圆，最终形成一个彩虹圈。
以上提示语为根据原始绘图命令整理而来，仅供参考。