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Rhombus Zolkowski

Rhombus Zolkowski
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2016-09-19 03:59
PolygonTrigonometryTransformation
This example demonstrates the construction of the Rhombus Zolkowski. Key mathematical concepts include the properties of a rhombus, angles, and trigonometry. Using GeoGebra commands such as Polygon, Angle, Rotate, etc., the dynamic transformation and properties of the rhombus are showcased. Suitable for middle school and above students to learn about geometric transformations and properties of rhombuses.

GeoGebra Commands & Parameters

  1. Polygon(A, B, C) → poly1, c, a, b
  2. Angle(C, B, A) → α
  3. Angle(A, C, B) → β
  4. Angle(B, A, C) → γ
  5. Line(A, B) → f
  6. Line(C, f) → g
  7. Point(g) → D
  8. Line(D, a) → h
  9. Line(D, b) → i
  10. Intersect(i, f) → E
  11. Intersect(h, f) → F
  12. Polygon(D, E, F) → poly2, f_1, d, e
  13. Line(G, H) → j
  14. Line(I, j) → k
  15. Line(H, I) → l
  16. Line(G, l) → m
  17. Intersect(m, k) → J
  18. Polygon(I, J, G, H) → poly3, i_1, j_1, g_1, h_1
  19. Polygon(L, K, N, M) → poly4, l_1, k_1, n, m_1
  20. Segment(K, M) → p
  21. Line(O, P) → q
  22. Rotate(O, 90°, P) → O'
  23. Angle(O, P, O') → δ
  24. Line(O', q) → r
  25. Line(P, O') → s
  26. Line(O, s) → t
  27. Intersect(t, r) → Q
  28. Polygon(P, O, Q, O') → poly5, p_1, o, q_1, o'
  29. Line(C_1, D_1) → e_1
  30. Line(E_1, e_1) → f_2
  31. Point(f_2) → F_1
  32. Line(C_1, F_1) → g_2
  33. Line(D_1, E_1) → h_2
  34. Polygon(D_1, C_1, F_1, E_1) → poly8, d_2, c_2, f_3, e_2
  35. Line(G_1, H_1) → i_2
  36. Line(G_1, I_1) → j_2
  37. OrthogonalLine(H_1, j_2) → k_2
  38. Line(I_1, i_2) → l_2
  39. Line(H_1, I_1) → m_2
  40. Line(G_1, m_2) → n_2
  41. Intersect(n_2, l_2) → J_1
  42. Intersect(k_2, l_2) → K_1
  43. Segment(L_1, M_1) → p_2
  44. Line(M_1, N_1) → q_2
  45. Line(L_1, N_1) → r_2
  46. OrthogonalLine(M_1, r_2) → g_3
  47. Line(N_1, p_2) → h_3
  48. Line(L_1, q_2) → i_3
  49. Intersect(g_3, i_3) → P_1
  50. Intersect(g_3, h_3) → O_1
  51. Intersect(i_3, g_3) → Q_1
  52. Polygon(M_1, O_1, N_1) → poly6, n_3, m_3, o_1
  53. Line(S, T) → n_1
  54. Point(Circle[T, Distance[S, T]]) → U
  55. Segment(T, U) → r_1
  56. Line(U, n_1) → s_1
  57. Line(S, r_1) → t_1
  58. Intersect(t_1, s_1) → V
  59. Polygon(S, T, U, V) → poly9, s_2, t_2, u, v