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Root Rectangles by Lecel Celec

Root Rectangles by Lecel Celec
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2019-04-21 15:40
Coordinate GeometryGeometric ConstructionSlider Animation
This example demonstrates the construction of root rectangles. A root rectangle is a special rectangle where the length of the diagonal is the geometric mean of its side lengths. Using GeoGebra commands such as Point, Segment, Polygon, etc., the properties of root rectangles can be dynamically illustrated. Suitable for middle school and above students to learn geometric construction and transformations.

GeoGebra Commands & Parameters

  1. Point(xAxis) → A
  2. Point(xAxis) → B
  3. Point(xAxis) → D
  4. Point(yAxis) → E
  5. Segment(O, P) → n
  6. Point(xAxis) → C
  7. Point(xAxis) → G
  8. Polygon(C, G, 4) → poly1, f, g, h, i, H, I
  9. Segment(C, H) → j
  10. Line(C, G) → k
  11. Circle(C, H) → c
  12. Intersect(c, k, 2) → J
  13. OrthogonalLine(J, k) → l
  14. Line(H, k) → m
  15. Intersect(l, m) → A_1
  16. Polygon(G, H, A_1, J) → q1, g_1, h_1, a_1, j_1
  17. Circle(C, A_1) → d
  18. Intersect(d, k, 2) → B_1
  19. Line(B_1, l) → p
  20. Intersect(m, p) → C_1
  21. Polygon(J, B_1, C_1, A_1) → q2, j_2, b_1, c_1, q
  22. Circle(C, C_1) → e
  23. Intersect(e, k, 2) → D_1
  24. Line(D_1, p) → r
  25. Intersect(m, r) → E_1
  26. Polygon(B_1, D_1, E_1, C_1) → q3, s, d_1, e_1, t
  27. Circle(C, E_1) → f_1
  28. Intersect(f_1, k, 2) → F_1
  29. Line(F_1, r) → a
  30. Intersect(m, a) → G_1
  31. Polygon(D_1, F_1, G_1, E_1) → q4, b, i_1, k_1, l_1
  32. Circle(C, G_1) → p_1
  33. Intersect(p_1, k, 2) → H_1
  34. Line(H_1, a) → m_1
  35. Intersect(m, m_1) → I_1
  36. Polygon(F_1, H_1, I_1, G_1) → q5, n_1, q_1, r_1, s_1
  37. Circle(C, I_1) → t_1
  38. Intersect(t_1, k, 2) → J_1
  39. Line(J_1, m_1) → f_2
  40. Intersect(m, f_2) → K_1
  41. Polygon(H_1, J_1, K_1, I_1) → q6, g_2, h_2, i_2, k_2
  42. Circle(C, K_1) → c_2
  43. Intersect(c_2, k, 2) → L_1
  44. Line(L_1, f_2) → l_2
  45. Intersect(m, l_2) → M_1
  46. Polygon(J_1, L_1, M_1, K_1) → q7, m_2, n_2, p_2, q_2
  47. Circle(C, M_1) → d_2
  48. Intersect(d_2, k, 2) → N_1
  49. Line(N_1, l_2) → r_2
  50. Intersect(m, r_2) → O_1
  51. Polygon(L_1, N_1, O_1, M_1) → q8, s_2, t_2, o_1, a_2
  52. CircleArc(C, J, H) → e_2
  53. CircleArc(C, B_1, A_1) → c_3
  54. CircleArc(C, D_1, C_1) → d_3
  55. CircleArc(C, F_1, E_1) → e_3
  56. CircleArc(C, J_1, I_1) → f_3
  57. CircleArc(C, H_1, G_1) → g_3
  58. CircleArc(C, L_1, K_1) → h_3
  59. CircleArc(C, N_1, M_1) → k_3