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Rhombus Stacking

Rhombus Stacking
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2017-03-16 03:52
PolygonTransformationGeometric Construction
This example demonstrates a geometry challenge involving rhombus stacking. Key mathematical concepts include rhombus, square, and geometric transformations. Using GeoGebra commands such as point, midpoint, intersect, segment, mirror, angle, polygon, etc., the construction of rhombus stacking is shown. Suitable for middle school and above students or teachers for teaching purposes.

GeoGebra Commands & Parameters

  1. Point(Ray[A, A + (1, 0)]) → B
  2. Point(Ray[B, B + (1, 0)]) → C
  3. Point(Ray[C, C + (1, 0)]) → D
  4. Point(Ray[D, D + (1, 0)]) → E
  5. Point(Ray[E, E + (1, 0)]) → F
  6. Midpoint(A, B) → G
  7. Intersect(Circle[A, d], Ray[G, G + (0, 1)]) → H,
  8. Point(Ray[H, H + (0, 1)]) → I
  9. Segment(A, I) → f
  10. Segment(B, I) → g
  11. Intersect(Circle[B, f], Ray[Midpoint[B, C], Midpoint[B, C] + (0, 1)]) → J,
  12. Intersect(Circle[C, f], Ray[Midpoint[D, C], Midpoint[D, C] + (0, 1)]) → K,
  13. Intersect(Circle[D, f], Ray[Midpoint[D, E], Midpoint[D, E] + (0, 1)]) → L, T
  14. Intersect(Circle[E, f], Ray[Midpoint[F, E], Midpoint[F, E] + (0, 1)]) → M,
  15. Segment(B, J) → h
  16. Segment(J, C) → i
  17. Segment(C, K) → j
  18. Segment(K, D) → k
  19. Segment(D, L) → l
  20. Segment(L, E) → m
  21. Segment(E, M) → n
  22. Segment(M, F) → p
  23. Mirror(B, Midpoint[I, J]) → B'
  24. Mirror(C, Midpoint[K, J]) → C'
  25. Mirror(D, Midpoint[K, L]) → D'
  26. Mirror(E, Midpoint[M, L]) → E'
  27. Segment(I, B') → q
  28. Segment(J, B') → r
  29. Segment(J, C') → s
  30. Segment(C', K) → t
  31. Segment(K, D') → a
  32. Segment(D', L) → b
  33. Segment(L, E') → c
  34. Segment(E', M) → e
  35. Mirror(J, Midpoint[B', C']) → J'
  36. Mirror(K, Midpoint[D', C']) → K'
  37. Mirror(L, Midpoint[D', E']) → L'
  38. Segment(B', J') → f_1
  39. Segment(J', C') → g_1
  40. Segment(C', K') → h_1
  41. Segment(K', D') → i_1
  42. Segment(D', L') → j_1
  43. Segment(L', E') → k_1
  44. Mirror(C', Midpoint[J', K']) → C''
  45. Mirror(D', Midpoint[L', K']) → D''
  46. Mirror(K', Midpoint[C'', D'']) → K''
  47. Segment(J', C'') → l_1
  48. Segment(C'', K') → m_1
  49. Segment(K', D'') → n_1
  50. Segment(D'', L') → p_1
  51. Segment(C'', K'') → q_1
  52. Segment(K'', D'') → r_1
  53. Angle(C'', K'', D'') → α
  54. Polygon(O, N, 4) → poly1, s_1, t_1, a_1, b_1, P, Q
  55. Circle(O, N) → d_1
  56. Circle(P, N) → e_1
  57. Intersect(d_1, c_1, 1) → R
  58. Intersect(e_1, c_1, 2) → S
  59. Segment(R, O) → f_2
  60. Segment(S, P) → g_2
  61. Angle(R, O, N) → β
  62. Angle(N, P, S) → γ
  63. Intersect(Circle[A, d'], Ray[G, G + (0, 1)]) → I',
  64. Segment(R, N) → h_2
  65. Angle(O, Q, P) → δ
  66. Segment(A, B) → i_2
  67. Segment(E, F) → j_2

AI Drawing Prompt Reference

Draw a stacked pattern of rhombuses. Start by placing points A, B, C, D, E, and F on a line. Then construct the vertices of each rhombus by finding intersection points and using reflections. Connect these points to form rhombuses, and use reflections to create more rhombuses, forming a stacked pattern.
The prompt above was compiled from the original drawing commands and is for reference only.