Rotating Hexagon

Rotating Hexagon
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2019-09-18 11:14
This example demonstrates the rotation of a hexagon. Key mathematical concepts include rotation, symmetry, circle, and trigonometry. Using GeoGebra commands such as Circle, Point, Segment, Line, Rotate, etc., a dynamic model of a rotating hexagon is constructed. Suitable for high school mathematics education, particularly in geometry and trigonometry.

GeoGebra Commands & Parameters

  1. Circle(A, B) → c
  2. Point(c) → C
  3. Segment(A, C) → f
  4. Point(c) → D
  5. Line(A, D) → g
  6. OrthogonalLine(C, g) → h
  7. Mirror(A, h) → A'
  8. Mirror(C, h) → C'
  9. Segment(A', C') → f'
  10. Point(g) → E
  11. Circle(E, A) → d
  12. Polygon(F, G, a) → poly1, i, s, t, b, H, I, J, K, L, M, N, j, O, P, Q, k, l, m, n, p, q, r
  13. Vector(H, A') → u
  14. Translate(poly1, u) → poly1'
  15. Rotate(poly1', 60°, E) → poly1''
  16. Rotate(A, 60°, E) → A'_1
  17. Rotate(C, 60°, E) → C'_1
  18. Segment(A'_1, C'_1) → f'_1
  19. Rotate(A', 60°, E) → A''
  20. Rotate(C', 60°, E) → C''
  21. Segment(A'', C'') → f''
  22. Rotate(poly1'', 60°, E) → poly1'''
  23. Rotate(A'_1, 60°, E) → R
  24. Rotate(C'_1, 60°, E) → S
  25. Segment(R, S) → e
  26. Rotate(A'', 60°, E) → A'''
  27. Rotate(C'', 60°, E) → C'''
  28. Segment(A''', C''') → f'''
  29. Rotate(poly1''', 60°, E) → t1
  30. Rotate(R, 60°, E) → R'
  31. Rotate(S, 60°, E) → S'
  32. Segment(R', S') → e'
  33. Rotate(A''', 60°, E) → T
  34. Rotate(C''', 60°, E) → U
  35. Segment(T, U) → f_1
  36. Rotate(t1, 60°, E) → t1'
  37. Rotate(R', 60°, E) → R''
  38. Rotate(S', 60°, E) → S''
  39. Segment(R'', S'') → e''
  40. Rotate(T, 60°, E) → T'
  41. Rotate(U, 60°, E) → U'
  42. Segment(T', U') → g_1
  43. Rotate(t1', 60°, E) → t1''
  44. Rotate(R'', 60°, E) → R'''
  45. Rotate(S'', 60°, E) → S'''
  46. Segment(R''', S''') → e'''
  47. Rotate(T', 60°, E) → T''
  48. Rotate(U', 60°, E) → U''
  49. Segment(T'', U'') → h_1
  50. Polygon(R, R', R'', R''', A, A'_1) → poly2, r_1, r', r'', r''', a_1, a'_1
  51. Circle(W, Z) → c_1
  52. Point(c_1) → A_1
  53. Point(c_1) → B_1
  54. Segment(A_1, B_1) → i_1
  55. Point(c_1) → C_1
  56. Segment(W, C_1) → j_1
  57. OrthogonalLine(C_1, i_1) → k_1
  58. Mirror(W, k_1) → W'
  59. Mirror(C_1, k_1) → D_1
  60. Segment(W', D_1) → l_1

AI Drawing Prompt Reference

Draw a rotating hexagon to demonstrate the concepts of rotation, symmetry, circle, and trigonometry. Start by drawing a circle and marking points on it to form one side of the hexagon. Then, rotate this side and the points to progressively build the rotating hexagon, showing its dynamic transformation.
The prompt above was compiled from the original drawing commands and is for reference only.