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根矩形与光

根矩形与光
几何画板及绘图内容加载中，请稍等……
2019-04-24 16:55
解析几何参数方程几何作图
该范例演示了根矩形与光的几何关系。涉及的核心数学概念包括根矩形的性质和光的路径。通过使用GeoGebra命令如Point, Segment, Polygon等进行几何作图。适合高中数学教学和学习。

GeoGebra 命令及参数

  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