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Twisted Tower of Polygons

Twisted Tower of Polygons
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2020-02-03 04:53
PolygonSequenceCoordinate Geometry
This example demonstrates a dynamic twisted tower structure composed of multiple polygons, showcasing their combination and transformation through adjustable parameters. Core mathematical concepts include polygon construction, coordinate geometry, sequence application, geometric transformations, and potential calculus concepts. It utilizes GeoGebra commands like Sequence, Polygon, and Element to dynamically visualize geometric changes. Suitable for high school and above, it aids in understanding polygon combinations, geometric transformations, and sequence applications.

GeoGebra Commands & Parameters

  1. Sequence((x(O) + (R * cos(i)), y(O) + (R * sin(i)), z(O)), i, 0, (2 * π), (2 * π / n)) → l2
  2. Polygon(l2) → poly1
  3. Sequence(Prism[Translate[Dilate[Rotate[poly1, (k * 6°)], 0.9^(k)], Vector[(0, 0, (k * 0.2))]], 0.2], k, 0, 60, 2) → l1
  4. Sequence(Prism[Translate[Dilate[Rotate[poly1, (k * 6°)], 0.9^(k)], Vector[(0, 0, (k * 0.2))]], 0.2], k, 0, 60) → l3
  5. Element(l3, A1) → B1
  6. Element(l3, A2) → B2
  7. Element(l3, A3) → B3
  8. Element(l3, A4) → B4
  9. Element(l3, A5) → B5
  10. Element(l3, A6) → B6
  11. Element(l3, A7) → B7
  12. Element(l3, A8) → B8
  13. Element(l3, A9) → B9
  14. Element(l3, A10) → B10
  15. Element(l3, A11) → B11
  16. Element(l3, A12) → B12
  17. Element(l3, A13) → B13
  18. Element(l3, A14) → B14
  19. Element(l3, A15) → B15
  20. Element(l3, A16) → B16
  21. Element(l3, A17) → B17
  22. Element(l3, A18) → B18
  23. Element(l3, A19) → B19
  24. Element(l3, A20) → B20
  25. Element(l3, A21) → B21
  26. Element(l3, A22) → B22
  27. Element(l3, A23) → B23
  28. Element(l3, A24) → B24
  29. Element(l3, A25) → B25
  30. Element(l3, A26) → B26
  31. Element(l3, A27) → B27
  32. Element(l3, A28) → B28
  33. Element(l3, A29) → B29
  34. Element(l3, A30) → B30
  35. Element(l3, A31) → B31
  36. Element(l3, A32) → B32
  37. Element(l3, A33) → B33
  38. Element(l3, A34) → B34
  39. Element(l3, A35) → B35
  40. Element(l3, A36) → B36
  41. Element(l3, A37) → B37
  42. Element(l3, A38) → B38
  43. Element(l3, A39) → B39
  44. Element(l3, A40) → B40
  45. Element(l3, A41) → B41
  46. Element(l3, A42) → B42
  47. Element(l3, A43) → B43
  48. Element(l3, A44) → B44
  49. Element(l3, A45) → B45
  50. Element(l3, A46) → B46
  51. Element(l3, A47) → B47
  52. Element(l3, A48) → B48
  53. Element(l3, A49) → B49
  54. Element(l3, A50) → B50
  55. Element(l3, A51) → B51
  56. Element(l3, A52) → B52
  57. Element(l3, A53) → B53
  58. Element(l3, A54) → B54
  59. Element(l3, A55) → B55
  60. Element(l3, A56) → B56
  61. Element(l3, A57) → B57
  62. Element(l3, A58) → B58
  63. Element(l3, A59) → B59
  64. Element(l3, A60) → B60

AI Drawing Prompt Reference

Create a dynamic twisted tower structure composed of multiple polygons, demonstrating their combination and transformation through adjustable parameters. Start by constructing a polygon based on parameters, then iteratively rotate, scale, and translate these polygons along the vertical axis to stack them layer by layer, forming a complex tower where each layer undergoes scaling and translation transformations.
The prompt above was compiled from the original drawing commands and is for reference only.