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P6 Symmetry Ex3: Slant Symmetrical Axis

P6 Symmetry Ex3: Slant Symmetrical Axis
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2020-05-26 20:33
TransformationGeometric Construction
This example demonstrates the construction of slant symmetrical axes in P6 symmetry, involving concepts of geometric symmetry, rotation symmetry, and combinatorics. The GeoGebra commands used include Segment, IndexOf, Mirror, and objects like Blue10b, Blue10a. Suitable for high school students learning geometric symmetry principles or for mathematical modeling education.

GeoGebra Commands & Parameters

  1. Segment(Blue10a, Blue10b) → Blue10
  2. Segment(Blue9a, Blue9b) → Blue9
  3. IndexOf(SelectedElement[ListNumSeg], ListNumSeg) → NumSeg
  4. Segment(Blue8a, Blue8b) → Blue8
  5. Segment(Blue7a, Blue7b) → Blue7
  6. Segment(Blue6a, Blue6b) → Blue6
  7. Segment(Blue5a, Blue5b) → Blue5
  8. Segment(Blue4a, Blue4b) → Blue4
  9. Segment(Blue3a, Blue3b) → Blue3
  10. Segment(Blue2a, Blue2b) → Blue2
  11. Segment(Blue1a, Blue1b) → Blue1
  12. IndexOf(SelectedElement[ListSymA], ListSymA) → NumSymA
  13. Element({SymA1, SymA2, SymA3, SymA4}, NumSymA) → SymA
  14. Mirror(Blue10b, SymA) → Blue10b'
  15. Mirror(Blue10a, SymA) → Blue10a'
  16. Segment(Blue10a', Blue10b') → RefBlue10
  17. Mirror(Blue9b, SymA) → Blue9b'
  18. Mirror(Blue9a, SymA) → Blue9a'
  19. Segment(Blue9a', Blue9b') → RefBlue9
  20. Mirror(Blue8b, SymA) → Blue8b'
  21. Mirror(Blue8a, SymA) → Blue8a'
  22. Segment(Blue8a', Blue8b') → RefBlue8
  23. Mirror(Blue7b, SymA) → Blue7b'
  24. Mirror(Blue7a, SymA) → Blue7a'
  25. Segment(Blue7a', Blue7b') → RefBlue7
  26. Mirror(Blue6b, SymA) → Blue6b'
  27. Mirror(Blue6a, SymA) → Blue6a'
  28. Segment(Blue6a', Blue6b') → RefBlue6
  29. Mirror(Blue5b, SymA) → Blue5b'
  30. Mirror(Blue5a, SymA) → Blue5a'
  31. Segment(Blue5a', Blue5b') → RefBlue5
  32. Mirror(Blue4b, SymA) → Blue4b'
  33. Mirror(Blue4a, SymA) → Blue4a'
  34. Segment(Blue4a', Blue4b') → RefBlue4
  35. Mirror(Blue3b, SymA) → Blue3b'
  36. Mirror(Blue3a, SymA) → Blue3a'
  37. Segment(Blue3a', Blue3b') → RefBlue3
  38. Mirror(Blue2b, SymA) → Blue2b'
  39. Mirror(Blue2a, SymA) → Blue2a'
  40. Segment(Blue2a', Blue2b') → RefBlue2
  41. Mirror(Blue1b, SymA) → Blue1b'
  42. Mirror(Blue1a, SymA) → Blue1a'
  43. Segment(Blue1a', Blue1b') → RefBlue1
  44. Defined(IndexOf[RefBlue1, List1]) → Match1
  45. Sequence(Sequence[(s, t), s, -14, 12], t, -8, 8) → ListDots
  46. If(NumSeg ≟ 1, Match1, NumSeg ≟ 6, Match6, NumSeg ≟ 7, Match7, NumSeg ≟ 8, Match8, NumSeg ≟ 9, Match9, Match10, NumSeg ≟ 2, Match2, NumSeg ≟ 3, Match3, NumSeg ≟ 4, Match4, NumSeg ≟ 5, Match5) → Match

AI Drawing Prompt Reference

Draw a P6 symmetric figure with multiple parallel line segments. Select one line segment and a symmetry axis, then mirror this line segment and its adjacent parallel segments to create symmetrical copies, finally connecting all segments and their mirrored versions to display the slant symmetry axis.
The prompt above was compiled from the original drawing commands and is for reference only.