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Root Rectangles and Light

Root Rectangles and Light
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2019-04-24 16:55
Coordinate GeometryParametric EquationGeometric Construction
This example demonstrates the geometric relationship between root rectangles and light. Key mathematical concepts include the properties of root rectangles and the path of light. It is constructed using GeoGebra commands such as Point, Segment, Polygon, etc. Suitable for high school mathematics education and learning.

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
  60. Point(yAxis) → P_1
  61. Polygon(P_1, Q_1, 4) → poly2, b_2, i_3, j_3, l_3, R_1, S_1
  62. Segment(P_1, E_1) → m_3
  63. Circle(P_1, E_1) → p_3
  64. Line(P_1, Q_1) → n_3
  65. Intersect(p_3, n_3, 2) → T_1
  66. Segment(T_1, L_1) → q_3
  67. CircleArc(P_1, T_1, E_1) → r_3
  68. Segment(Q_1, T_1) → s_3
  69. Segment(Q_1, D_1) → t_3
  70. Polygon(U_1, V_1, 4) → poly3, a_3, b_3, f_4, g_4, W_1, Z_1
  71. Segment(U_1, O_1) → h_4
  72. Line(U_1, V_1) → i_4
  73. Circle(U_1, O_1) → c_4
  74. Intersect(c_4, i_4, 2) → A_2
  75. OrthogonalLine(A_2, i_4) → j_4
  76. Line(I, O_1) → k_4
  77. Intersect(j_4, k_4) → B_2
  78. Segment(V_1, A_2) → l_4
  79. Segment(A_2, B_2) → m_4
  80. Segment(B_2, O_1) → n_4
  81. Segment(V_1, N_1) → p_4
  82. CircleArc(U_1, A_2, O_1) → d_4
  83. Line(A_2, T_1) → q_4
  84. Line(V_1, Q_1) → r_4
  85. Circle(P_1, M_1) → e_4
  86. Circle(U_1, B_2) → s_4
  87. Line(P_1, T_1) → t_4
  88. Line(U_1, A_2) → a_4
  89. Line(I, B_2) → b_4
  90. Intersect(s_4, a_4, 2) → C_2
  91. Intersect(e_4, t_4, 2) → D_2
  92. OrthogonalLine(D_2, t_4) → f_5
  93. OrthogonalLine(C_2, a_4) → g_5
  94. Intersect(b_4, f_5) → E_2
  95. Intersect(b_4, g_5) → F_2
  96. Segment(T_1, D_2) → h_5
  97. Segment(D_2, E_2) → i_5
  98. Segment(A_2, C_2) → j_5
  99. Segment(C_2, F_2) → k_5
  100. Segment(F_2, B_2) → l_5
  101. CircleArc(P_1, D_2, M_1) → c_5
  102. CircleArc(U_1, C_2, B_2) → d_5
  103. Line(I, C_2) → m_5
  104. Line(I, D_1) → n_5
  105. Line(I, F_1) → p_5
  106. Line(I, H_1) → q_5
  107. Line(I, J_1) → r_5
  108. Line(I, L_1) → s_5
  109. Line(I, N_1) → t_5
  110. Line(P_1, Q_1) → a_5
  111. Intersect(n_5, a_5) → G_2
  112. Intersect(p_5, a_5) → H_2
  113. Intersect(q_5, a_5) → I_2
  114. Intersect(r_5, a_5) → J_2
  115. Intersect(s_5, a_5) → K_2
  116. Intersect(t_5, a_5) → L_2
  117. Line(S_1, M_2) → b_5
  118. Line(S_1, N_2) → e_5
  119. Line(S_1, O_2) → f_6
  120. Line(S_1, P_2) → g_6
  121. Line(S_1, Q_2) → h_6
  122. Line(S_1, R_2) → i_6
  123. Line(S_1, S_2) → j_6
  124. Line(S_1, T_2) → k_6
  125. Line(S_1, U_2) → l_6
  126. Line(U_1, C_2) → m_6
  127. Intersect(n_5, m_6) → V_2
  128. Intersect(q_4, r_4) → W_2