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Symmetry Number for Double Octagons

Symmetry Number for Double Octagons
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2019-06-17 03:12
PolygonTransformationGeometric Construction
This example demonstrates the symmetry of double octagons. Key mathematical concepts include geometric transformations, symmetry, and polygons. Using GeoGebra commands such as Circle, Point, Segment, Rotate, etc., the construction of double octagons and the observation of their symmetry are illustrated. Suitable for middle school and above students or teachers.

GeoGebra Commands & Parameters

  1. Circle(A, a) → c
  2. Circle(B, b) → d
  3. Point(c) → C
  4. Point(d) → D
  5. Segment(A, C) → g
  6. Segment(B, D) → h
  7. Rotate(C, 45°, A) → C'
  8. Angle(C, A, C') → α
  9. Segment(A, C') → i
  10. Rotate(C', 45°, A) → C''
  11. Angle(C', A, C'') → β
  12. Segment(A, C'') → j
  13. Rotate(C'', 45°, A) → C'''
  14. Angle(C'', A, C''') → γ
  15. Segment(C''', A) → k
  16. Segment(C''', A) → l
  17. Segment(C''', A) → m
  18. Rotate(C''', 45°, A) → E
  19. Angle(C''', A, E) → δ
  20. Segment(A, E) → n
  21. Rotate(E, 45°, A) → E'
  22. Angle(E, A, E') → ε
  23. Segment(E', A) → p
  24. Rotate(E', 45°, A) → E''
  25. Angle(E', A, E'') → ζ
  26. Segment(A, E'') → q
  27. Rotate(E'', 45°, A) → E'''
  28. Angle(E'', A, E''') → η
  29. Segment(A, E''') → r
  30. Rotate(D, 45°, B) → D'
  31. Angle(D, B, D') → θ
  32. Segment(B, D') → s
  33. Rotate(D', 45°, B) → D''
  34. Angle(D', B, D'') → ι
  35. Segment(B, D'') → t
  36. Rotate(D'', 45°, B) → D'''
  37. Angle(D'', B, D''') → κ
  38. Segment(B, D''') → f_1
  39. Rotate(D''', 45°, B) → F
  40. Angle(D''', B, F) → λ
  41. Segment(B, F) → g_1
  42. Rotate(F, 45°, B) → F'
  43. Angle(F, B, F') → μ
  44. Segment(F', B) → h_1
  45. Rotate(F', 45°, B) → F''
  46. Angle(F', B, F'') → ν
  47. Segment(B, F'') → i_1
  48. Rotate(F'', 45°, B) → F'''
  49. Angle(F'', B, F''') → ξ
  50. Segment(B, F''') → j_1
  51. Segment(C''', B) → k_1
  52. Segment(E, B) → l_1
  53. Segment(E', B) → m_1
  54. Segment(E'', B) → n_1
  55. Segment(E''', B) → p_1
  56. Segment(C, B) → q_1
  57. Segment(C', B) → r_1
  58. Segment(C'', B) → s_1
  59. Segment(D, A) → t_1
  60. Segment(F''', A) → a_1
  61. Segment(F'', A) → b_1
  62. Segment(F', A) → c_1
  63. Segment(F, A) → d_1
  64. Segment(D''', A) → e_1
  65. Segment(D'', A) → f_2
  66. Segment(D', A) → g_2