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Create Symmetrical Shapes

Create Symmetrical Shapes
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2020-05-05 12:09
In collections P6 6S1 對稱 (中文版)
This example demonstrates how to create symmetrical shapes using GeoGebra. Key mathematical concepts include symmetry, reflection, and similar triangles. Using commands like IndexOf, Element, Mirror, and Segment, multiple symmetrical shapes can be constructed. Suitable for middle school and above students learning geometric transformations.

GeoGebra Commands & Parameters

  1. IndexOf(SelectedElement[ListSymA], ListSymA) → NumSymA
  2. Element({SymA1, SymA2, SymA3, SymA4}, NumSymA) → SymA
  3. Mirror(Blue01a, SymA) → Blue01aR
  4. Mirror(Blue01b, SymA) → Blue01bR
  5. Segment(Blue01aR, Blue01bR) → RefBlue1
  6. Segment(Blue01a, Blue01b) → Blue1
  7. Defined(IndexOf[RefBlue1, List1]) → Match1
  8. Mirror(Blue02a, SymA) → Blue02aR
  9. Mirror(Blue02b, SymA) → Blue02bR
  10. Segment(Blue02aR, Blue02bR) → RefBlue2
  11. Segment(Blue02a, Blue02b) → Blue2
  12. Mirror(Blue03a, SymA) → Blue03aR
  13. Mirror(Blue03b, SymA) → Blue03bR
  14. Segment(Blue03aR, Blue03bR) → RefBlue3
  15. Segment(Blue03a, Blue03b) → Blue3
  16. Mirror(Blue04a, SymA) → Blue04aR
  17. Mirror(Blue04b, SymA) → Blue04bR
  18. Segment(Blue04aR, Blue04bR) → RefBlue4
  19. Segment(Blue04a, Blue04b) → Blue4
  20. Mirror(Blue05a, SymA) → Blue05aR
  21. Mirror(Blue05b, SymA) → Blue05bR
  22. Segment(Blue05aR, Blue05bR) → RefBlue5
  23. Segment(Blue05a, Blue05b) → Blue5
  24. Mirror(Blue06a, SymA) → Blue06aR
  25. Mirror(Blue06b, SymA) → Blue06bR
  26. Segment(Blue06aR, Blue06bR) → RefBlue6
  27. Segment(Blue06a, Blue06b) → Blue6
  28. Mirror(Blue07a, SymA) → Blue07aR
  29. Mirror(Blue07b, SymA) → Blue07bR
  30. Segment(Blue07aR, Blue07bR) → RefBlue7
  31. Segment(Blue07a, Blue07b) → Blue7
  32. Mirror(Blue08a, SymA) → Blue08aR
  33. Mirror(Blue08b, SymA) → Blue08bR
  34. Segment(Blue08aR, Blue08bR) → RefBlue8
  35. Segment(Blue08a, Blue08b) → Blue8
  36. IndexOf(SelectedElement[ListNumSeg], ListNumSeg) → NumSeg
  37. Mirror(Blue09a, SymA) → Blue09aR
  38. Mirror(Blue09b, SymA) → Blue09bR
  39. Segment(Blue09aR, Blue09bR) → RefBlue9
  40. Segment(Blue09a, Blue09b) → Blue9
  41. Mirror(Blue10a, SymA) → Blue10aR
  42. Mirror(Blue10b, SymA) → Blue10bR
  43. Segment(Blue10aR, Blue10bR) → RefBlue10
  44. Segment(Blue10a, Blue10b) → Blue10
  45. Mirror(Blue11a, SymA) → Blue11aR
  46. Mirror(Blue11b, SymA) → Blue11bR
  47. Segment(Blue11aR, Blue11bR) → RefBlue11
  48. Segment(Blue11a, Blue11b) → Blue11
  49. Mirror(Blue12a, SymA) → Blue12aR
  50. Mirror(Blue12b, SymA) → Blue12bR
  51. Segment(Blue12aR, Blue12bR) → RefBlue12
  52. Segment(Blue12a, Blue12b) → Blue12
  53. Sequence(Sequence[(s, t), s, -14, 12], t, -8, 8) → ListDots
  54. If(NumSeg ≟ 1, Match1, NumSeg ≟ 6, Match6, NumSeg ≟ 7, Match7, NumSeg ≟ 8, Match8, NumSeg ≟ 9, Match9, NumSeg ≟ 10, Match10, NumSeg ≟ 2, NumSeg ≟ 11, Match11, Match12, Match2, NumSeg ≟ 3, Match3, NumSeg ≟ 4, Match4, NumSeg ≟ 5, Match5) → Match

AI Drawing Prompt Reference

Draw a set of symmetrical shapes: first define a symmetry axis, then place several blue segments on one side, each determined by two endpoints. Reflect these segments across the axis to get corresponding reflected segments. Then connect each original segment with its reflected counterpart using line segments, forming closed symmetrical shapes. Repeat this process to construct multiple groups, each containing two original segments, two reflected segments, and connecting lines, resulting in a series of mirror-symmetric geometric patterns about the same axis.
The prompt above was compiled from the original drawing commands and is for reference only.