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列表项轻松着色

列表项轻松着色
几何画板及绘图内容加载中，请稍等……
2020-01-24 04:23
多边形解析几何立体几何几何作图
所属专题 Color 3D surfaces
①本范例演示如何在 GeoGebra 中对列表中的图形项进行着色；②涉及核心数学概念包括多边形、立体几何、解析几何；③作图要点：使用了 Polygon（多边形）、Prism（棱柱）、Midpoint（中点）、Circle（圆）、Line（直线）、Sequence（数列）、Rotate（旋转）等命令和对象；④适合高中及以上学生学习和探索几何图形的属性与变换。

GeoGebra 命令及参数

  1. Polygon(A, B, 4, xOyPlane) → poly1, f, g, h, i, C, D
  2. Prism(poly1, 0.2) → a, E, edge1, edge2, edge3, edge4, edge5, edge6, edge7, edge8, F, G, H, face1, face2, face3, face4, face5
  3. Midpoint(D, B) → L
  4. Circle(yAxis, L) → c
  5. Midpoint(E, G) → J
  6. Line(L, J) → j
  7. Sequence(Rotate[j, (w * π / 36), yAxis], w, 1, 72) → L_2
  8. Rotate(A, b, L) → AA
  9. Rotate(B, b, L) → BB
  10. Polygon(AA, BB, 4, xOyPlane) → poly2, k, l, m, n_1, I, K
  11. Prism(poly2, 0.2) → d, M, arêteAAM, arêteBBN, arêteIO, arêteKP, arêteMN, arêteNO, arêteOP, arêteMP, N, O, P, faceAABBNM, faceBBION, faceIKPO, faceAAKPM, faceMNOP
  12. Rotate(Rotate[d, (A1 * π / (n / 2)), yAxis], (A1 * π / (n / 4)), Element[L_2, A1]) → B1
  13. Rotate(Rotate[d, (A2 * π / (n / 2)), yAxis], (A2 * π / (n / 4)), Element[L_2, A2]) → B2
  14. Rotate(Rotate[d, (A3 * π / (n / 2)), yAxis], (A3 * π / (n / 4)), Element[L_2, A3]) → B3
  15. Rotate(Rotate[d, (A4 * π / (n / 2)), yAxis], (A4 * π / (n / 4)), Element[L_2, A4]) → B4
  16. Rotate(Rotate[d, (A5 * π / (n / 2)), yAxis], (A5 * π / (n / 4)), Element[L_2, A5]) → B5
  17. Rotate(Rotate[d, (A6 * π / (n / 2)), yAxis], (A6 * π / (n / 4)), Element[L_2, A6]) → B6
  18. Rotate(Rotate[d, (A7 * π / (n / 2)), yAxis], (A7 * π / (n / 4)), Element[L_2, A7]) → B7
  19. Rotate(Rotate[d, (A8 * π / (n / 2)), yAxis], (A8 * π / (n / 4)), Element[L_2, A8]) → B8
  20. Rotate(Rotate[d, (A9 * π / (n / 2)), yAxis], (A9 * π / (n / 4)), Element[L_2, A9]) → B9
  21. Rotate(Rotate[d, (A10 * π / (n / 2)), yAxis], (A10 * π / (n / 4)), Element[L_2, A10]) → B10
  22. Rotate(Rotate[d, (A11 * π / (n / 2)), yAxis], (A11 * π / (n / 4)), Element[L_2, A11]) → B11
  23. Rotate(Rotate[d, (A12 * π / (n / 2)), yAxis], (A12 * π / (n / 4)), Element[L_2, A12]) → B12
  24. Rotate(Rotate[d, (A13 * π / (n / 2)), yAxis], (A13 * π / (n / 4)), Element[L_2, A13]) → B13
  25. Rotate(Rotate[d, (A14 * π / (n / 2)), yAxis], (A14 * π / (n / 4)), Element[L_2, A14]) → B14
  26. Rotate(Rotate[d, (A15 * π / (n / 2)), yAxis], (A15 * π / (n / 4)), Element[L_2, A15]) → B15
  27. Rotate(Rotate[d, (A16 * π / (n / 2)), yAxis], (A16 * π / (n / 4)), Element[L_2, A16]) → B16
  28. Rotate(Rotate[d, (A17 * π / (n / 2)), yAxis], (A17 * π / (n / 4)), Element[L_2, A17]) → B17
  29. Rotate(Rotate[d, (A18 * π / (n / 2)), yAxis], (A18 * π / (n / 4)), Element[L_2, A18]) → B18
  30. Rotate(Rotate[d, (A19 * π / (n / 2)), yAxis], (A19 * π / (n / 4)), Element[L_2, A19]) → B19
  31. Rotate(Rotate[d, (A20 * π / (n / 2)), yAxis], (A20 * π / (n / 4)), Element[L_2, A20]) → B20
  32. Rotate(Rotate[d, (A21 * π / (n / 2)), yAxis], (A21 * π / (n / 4)), Element[L_2, A21]) → B21
  33. Rotate(Rotate[d, (A22 * π / (n / 2)), yAxis], (A22 * π / (n / 4)), Element[L_2, A22]) → B22
  34. Rotate(Rotate[d, (A23 * π / (n / 2)), yAxis], (A23 * π / (n / 4)), Element[L_2, A23]) → B23
  35. Rotate(Rotate[d, (A24 * π / (n / 2)), yAxis], (A24 * π / (n / 4)), Element[L_2, A24]) → B24
  36. Rotate(Rotate[d, (A25 * π / (n / 2)), yAxis], (A25 * π / (n / 4)), Element[L_2, A25]) → B25
  37. Rotate(Rotate[d, (A26 * π / (n / 2)), yAxis], (A26 * π / (n / 4)), Element[L_2, A26]) → B26
  38. Rotate(Rotate[d, (A27 * π / (n / 2)), yAxis], (A27 * π / (n / 4)), Element[L_2, A27]) → B27
  39. Rotate(Rotate[d, (A28 * π / (n / 2)), yAxis], (A28 * π / (n / 4)), Element[L_2, A28]) → B28
  40. Rotate(Rotate[d, (A29 * π / (n / 2)), yAxis], (A29 * π / (n / 4)), Element[L_2, A29]) → B29
  41. Rotate(Rotate[d, (A30 * π / (n / 2)), yAxis], (A30 * π / (n / 4)), Element[L_2, A30]) → B30
  42. Rotate(Rotate[d, (A31 * π / (n / 2)), yAxis], (A31 * π / (n / 4)), Element[L_2, A31]) → B31
  43. Rotate(Rotate[d, (A32 * π / (n / 2)), yAxis], (A32 * π / (n / 4)), Element[L_2, A32]) → B32
  44. Rotate(Rotate[d, (A33 * π / (n / 2)), yAxis], (A33 * π / (n / 4)), Element[L_2, A33]) → B33
  45. Rotate(Rotate[d, (A34 * π / (n / 2)), yAxis], (A34 * π / (n / 4)), Element[L_2, A34]) → B34
  46. Rotate(Rotate[d, (A35 * π / (n / 2)), yAxis], (A35 * π / (n / 4)), Element[L_2, A35]) → B35
  47. Rotate(Rotate[d, (A36 * π / (n / 2)), yAxis], (A36 * π / (n / 4)), Element[L_2, A36]) → B36
  48. Rotate(Rotate[d, (A37 * π / (n / 2)), yAxis], (A37 * π / (n / 4)), Element[L_2, A37]) → B37
  49. Rotate(Rotate[d, (A38 * π / (n / 2)), yAxis], (A38 * π / (n / 4)), Element[L_2, A38]) → B38
  50. Rotate(Rotate[d, (A39 * π / (n / 2)), yAxis], (A39 * π / (n / 4)), Element[L_2, A39]) → B39
  51. Rotate(Rotate[d, (A40 * π / (n / 2)), yAxis], (A40 * π / (n / 4)), Element[L_2, A40]) → B40
  52. Rotate(Rotate[d, (A41 * π / (n / 2)), yAxis], (A41 * π / (n / 4)), Element[L_2, A41]) → B41
  53. Rotate(Rotate[d, (A42 * π / (n / 2)), yAxis], (A42 * π / (n / 4)), Element[L_2, A42]) → B42
  54. Rotate(Rotate[d, (A43 * π / (n / 2)), yAxis], (A43 * π / (n / 4)), Element[L_2, A43]) → B43
  55. Rotate(Rotate[d, (A44 * π / (n / 2)), yAxis], (A44 * π / (n / 4)), Element[L_2, A44]) → B44
  56. Rotate(Rotate[d, (A45 * π / (n / 2)), yAxis], (A45 * π / (n / 4)), Element[L_2, A45]) → B45
  57. Rotate(Rotate[d, (A46 * π / (n / 2)), yAxis], (A46 * π / (n / 4)), Element[L_2, A46]) → B46
  58. Rotate(Rotate[d, (A47 * π / (n / 2)), yAxis], (A47 * π / (n / 4)), Element[L_2, A47]) → B47
  59. Rotate(Rotate[d, (A48 * π / (n / 2)), yAxis], (A48 * π / (n / 4)), Element[L_2, A48]) → B48
  60. Rotate(Rotate[d, (A49 * π / (n / 2)), yAxis], (A49 * π / (n / 4)), Element[L_2, A49]) → B49
  61. Rotate(Rotate[d, (A50 * π / (n / 2)), yAxis], (A50 * π / (n / 4)), Element[L_2, A50]) → B50
  62. Rotate(Rotate[d, (A51 * π / (n / 2)), yAxis], (A51 * π / (n / 4)), Element[L_2, A51]) → B51
  63. Rotate(Rotate[d, (A52 * π / (n / 2)), yAxis], (A52 * π / (n / 4)), Element[L_2, A52]) → B52
  64. Rotate(Rotate[d, (A53 * π / (n / 2)), yAxis], (A53 * π / (n / 4)), Element[L_2, A53]) → B53
  65. Rotate(Rotate[d, (A54 * π / (n / 2)), yAxis], (A54 * π / (n / 4)), Element[L_2, A54]) → B54
  66. Rotate(Rotate[d, (A55 * π / (n / 2)), yAxis], (A55 * π / (n / 4)), Element[L_2, A55]) → B55
  67. Rotate(Rotate[d, (A56 * π / (n / 2)), yAxis], (A56 * π / (n / 4)), Element[L_2, A56]) → B56
  68. Rotate(Rotate[d, (A57 * π / (n / 2)), yAxis], (A57 * π / (n / 4)), Element[L_2, A57]) → B57
  69. Rotate(Rotate[d, (A58 * π / (n / 2)), yAxis], (A58 * π / (n / 4)), Element[L_2, A58]) → B58
  70. Rotate(Rotate[d, (A59 * π / (n / 2)), yAxis], (A59 * π / (n / 4)), Element[L_2, A59]) → B59
  71. Rotate(Rotate[d, (A60 * π / (n / 2)), yAxis], (A60 * π / (n / 4)), Element[L_2, A60]) → B60
  72. Rotate(Rotate[d, (A61 * π / (n / 2)), yAxis], (A61 * π / (n / 4)), Element[L_2, A61]) → B61
  73. Rotate(Rotate[d, (A62 * π / (n / 2)), yAxis], (A62 * π / (n / 4)), Element[L_2, A62]) → B62
  74. Rotate(Rotate[d, (A63 * π / (n / 2)), yAxis], (A63 * π / (n / 4)), Element[L_2, A63]) → B63
  75. Rotate(Rotate[d, (A64 * π / (n / 2)), yAxis], (A64 * π / (n / 4)), Element[L_2, A64]) → B64
  76. Rotate(Rotate[d, (A65 * π / (n / 2)), yAxis], (A65 * π / (n / 4)), Element[L_2, A65]) → B65
  77. Rotate(Rotate[d, (A66 * π / (n / 2)), yAxis], (A66 * π / (n / 4)), Element[L_2, A66]) → B66
  78. Rotate(Rotate[d, (A67 * π / (n / 2)), yAxis], (A67 * π / (n / 4)), Element[L_2, A67]) → B67
  79. Rotate(Rotate[d, (A68 * π / (n / 2)), yAxis], (A68 * π / (n / 4)), Element[L_2, A68]) → B68
  80. Rotate(Rotate[d, (A69 * π / (n / 2)), yAxis], (A69 * π / (n / 4)), Element[L_2, A69]) → B69
  81. Rotate(Rotate[d, (A70 * π / (n / 2)), yAxis], (A70 * π / (n / 4)), Element[L_2, A70]) → B70
  82. Rotate(Rotate[d, (A71 * π / (n / 2)), yAxis], (A71 * π / (n / 4)), Element[L_2, A71]) → B71
  83. Rotate(Rotate[d, (A72 * π / (n / 2)), yAxis], (A72 * π / (n / 4)), Element[L_2, A72]) → B72

AI 绘图提示语参考

画一个四边形，然后以该四边形为基础构造一个棱柱。接着找到棱柱的一个顶点和四边形的一个顶点的中点，并以此中点为圆心画一个圆。再找到棱柱的另外两个顶点的中点，并连接这两个中点形成一条直线。最后，将这条直线绕Y轴旋转72次，每次旋转角度为π/36，得到一系列旋转后的直线。
以上提示语为根据原始绘图命令整理而来，仅供参考。