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Easily Color List Items

Easily Color List Items
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2020-01-24 04:23
PolygonCoordinate GeometrySolid GeometryGeometric Construction
In collections Color 3D surfaces
This example demonstrates how to easily color items in a list within GeoGebra, focusing on geometric constructions and properties. It involves core math concepts like polygons, solid geometry, and coordinate geometry. Key GeoGebra commands and objects used include Polygon, Prism, Midpoint, Circle, Line, Sequence, and Rotate. Suitable for high school and above students exploring geometric attributes and transformations.

GeoGebra Commands & Parameters

  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 Drawing Prompt Reference

Draw a quadrilateral and construct a prism based on it. Then find the midpoint of one vertex of the prism and one vertex of the quadrilateral, and draw a circle centered at this midpoint. Next, find the midpoints of the other two vertices of the prism, connect these midpoints to form a line, and rotate this line around the Y-axis 72 times, each rotation being π/36 degrees, to obtain a series of rotated lines.
The prompt above was compiled from the original drawing commands and is for reference only.