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GeoGebra几何作图与图形分析

GeoGebra几何作图与图形分析
几何画板及绘图内容加载中，请稍等……
2020-05-14 00:25
圆多边形解析几何几何作图
该范例展示了如何使用GeoGebra进行几何图形构造与分析。核心数学概念包括多边形、圆、向量和坐标几何。作图要点涉及Polygon、Segment、Line、CircleArc等命令，以及Point、Intersect等对象。适合初中或高中数学教学，用于理解几何变换和图形性质。

GeoGebra 命令及参数

  1. Polygon(A, C, D, B) → vierhoek1, a, c, d, b
  2. Polygon(E, P, Q, F) → vierhoek2, e, p, q, f
  3. Polygon(P, N, O, Q) → vierhoek3, p_1, n, o, q_1
  4. Segment(E, A) → g
  5. Segment(G, C) → h
  6. Segment(H, D) → i
  7. Line(L, M) → j
  8. CircleArc(L, N, G) → k
  9. CircleArc(M, O, H) → r
  10. Segment(G, H) → l
  11. Point(k) → R
  12. Point(k) → S
  13. Point(k) → T
  14. Point(k) → U
  15. Point(k) → G_1
  16. Point(k) → H_1
  17. Point(k) → I_1
  18. Point(k) → J_1
  19. Line(R, l) → m
  20. Line(S, l) → s
  21. Line(T, j) → t
  22. Line(U, j) → f_1
  23. Line(J_1, j) → g_1
  24. Line(I_1, j) → h_1
  25. Line(H_1, j) → i_1
  26. Line(G_1, j) → j_1
  27. Intersect(j_1, r) → V,
  28. Intersect(i_1, r) → W,
  29. Intersect(h_1, r) → Z,
  30. Intersect(g_1, r) → A_1,
  31. Intersect(f_1, r) → B_1,
  32. Intersect(t, r) → C_1,
  33. Intersect(s, r) → D_1,
  34. Intersect(m, r) → E_1,
  35. Polygon(G, H, E_1, R) → vierhoek4, g_2, h_2, e_1, r_1
  36. Polygon(S, R, E_1, D_1) → vierhoek5, s_1, r_2, k_1, d_1
  37. Polygon(T, S, D_1, C_1) → vierhoek6, t_1, s_2, l_1, c_1
  38. Polygon(U, T, C_1, B_1) → vierhoek7, u, t_2, m_1, b_1
  39. Polygon(J_1, U, B_1, A_1) → vierhoek8, n_1, u_1, a_1, f_2
  40. Polygon(I_1, J_1, A_1, Z) → vierhoek9, i_2, j_2, k_2, z_1
  41. Polygon(H_1, I_1, Z, W) → vierhoek10, l_2, m_2, z_2, w
  42. Polygon(G_1, H_1, W, V) → vierhoek11, n_2, p_2, w_1, v
  43. Polygon(N, G_1, V, O) → vierhoek12, n_3, q_2, v_1, o_1
  44. Line(N, e) → a_2
  45. Line(G_1, e) → b_2
  46. Line(H_1, e) → c_2
  47. Line(I_1, e) → d_2
  48. Line(J_1, e) → e_2
  49. Line(U, e) → f_3
  50. Line(T, e) → g_3
  51. Line(S, e) → h_3
  52. Line(R, e) → i_3
  53. Line(G, e) → j_3
  54. Intersect(a_2, g) → F_1
  55. Intersect(g, c_2) → L_1
  56. Intersect(d_2, g) → M_1
  57. Intersect(g, e_2) → N_1
  58. Intersect(g, f_3) → O_1
  59. Intersect(g, g_3) → P_1
  60. Intersect(g, h_3) → Q_1
  61. Intersect(g, i_3) → R_1
  62. Intersect(g, j_3) → S_1
  63. Polygon(E, F_1, N, P) → vierhoek13, e_3, k_3, n_4, p_3
  64. Line(G_1, p_3) → l_3
  65. Intersect(l_3, g) → K_1
  66. Polygon(F_1, K_1, G_1, N) → vierhoek14, m_3, q_3, r_3, n_5
  67. Polygon(K_1, L_1, H_1, G_1) → vierhoek15, s_3, t_3, a_3, b_3
  68. Polygon(L_1, M_1, I_1, H_1) → vierhoek16, c_3, d_3, f_4, g_4
  69. Polygon(M_1, N_1, J_1, I_1) → vierhoek17, h_4, i_4, j_4, k_4
  70. Polygon(N_1, O_1, U, J_1) → vierhoek18, l_4, m_4, u_2, p_4
  71. Polygon(O_1, P_1, T, U) → vierhoek19, q_4, r_4, t_4, u_3
  72. Polygon(P_1, Q_1, S, T) → vierhoek20, s_4, a_4, s_5, t_5
  73. Polygon(Q_1, R_1, R, S) → vierhoek21, b_4, c_4, r_5, s_6
  74. Polygon(R_1, S_1, G, R) → vierhoek22, d_4, e_4, g_5, r_6
  75. Polygon(S_1, A, C, G) → vierhoek23, f_5, a_5, c_5, g_6
  76. Segment(F, B) → h_5
  77. Line(O, q) → i_5
  78. Line(V, q) → j_5
  79. Line(W, q) → k_5
  80. Line(Z, q) → l_5
  81. Line(A_1, q) → m_5
  82. Line(B_1, q) → p_5
  83. Line(C_1, q) → q_5
  84. Line(D_1, q) → b_5
  85. Line(E_1, q) → d_5
  86. Line(H, q) → e_5
  87. Intersect(h_5, i_5) → T_1
  88. Intersect(j_5, h_5) → U_1
  89. Intersect(k_5, h_5) → V_1
  90. Intersect(l_5, h_5) → W_1
  91. Intersect(m_5, h_5) → Z_1
  92. Intersect(h_5, p_5) → A_2
  93. Intersect(h_5, q_5) → B_2
  94. Intersect(h_5, b_5) → C_2
  95. Intersect(d_5, h_5) → D_2
  96. Intersect(h_5, e_5) → E_2
  97. Polygon(Q, O, T_1, F) → vierhoek24, q_6, o_2, f_6, f_7
  98. Polygon(O, V) → veelhoek1, o_3, v_2
  99. Polygon(O, V, U_1, T_1) → vierhoek25, o_4, v_3, h_6, i_6
  100. Polygon(V, W, V_1, U_1) → vierhoek26, v_4, w_2, j_6, k_6
  101. Polygon(W, Z, W_1, V_1) → vierhoek27, w_3, z_3, l_6, m_6
  102. Polygon(Z, A_1, Z_1, W_1) → vierhoek28, z_4, n_6, p_6, t_6
  103. Polygon(A_1, B_1, A_2, Z_1) → vierhoek29, a_6, b_6, c_6, d_6
  104. Polygon(B_1, C_1, B_2, A_2) → vierhoek30, e_6, g_7, h_7, i_7
  105. Polygon(C_1, D_1, C_2, B_2) → vierhoek31, j_7, k_7, l_7, m_7
  106. Polygon(D_1, E_1, D_2, C_2) → vierhoek32, n_7, p_7, q_7, r_7
  107. Polygon(E_1, H, E_2, D_2) → vierhoek33, s_7, h_8, t_7, a_7
  108. Polygon(G, C, D, H) → vierhoek34, g_8, c_7, d_7, h_9
  109. Polygon(D, B, E_2, H) → vierhoek35, d_8, b_7, e_7, h_{10}
  110. Polygon(B, A, E, F) → vierhoek36, b_8, a_8, e_8, f_8
  111. Segment(P, Q) → i_8
  112. Segment(P, E) → j_8
  113. Segment(N, O) → k_8
  114. Segment(C, D) → l_8
  115. Surface((0.8 * cos(tt)) + 1, hh, (0.8 * sin(tt)) + 1, tt, 0°, 180°, hh, -1, 1) → u_4
  116. Polygon((0.2, -1, 0), (0.2, 1, 0), (0.2, 1, 1), (0.2, -1, 1)) → vierhoek37, m_8, n_8, p_8, q_8
  117. Translate(vierhoek37, Vector[(1.6, 0, 0)]) → vierhoek37'
  118. Translate(q_8, Vector[(1.6, 0, 0)]) → r_8
  119. Translate(n_8, Vector[(1.6, 0, 0)]) → s_8
  120. Translate(m_8, Vector[(1.6, 0, 0)]) → t_8

AI 绘图提示语参考

请绘制一个由多个四边形组成的复杂几何图形。图形包括一个矩形、一个平行四边形和一些三角形。这些图形通过线段、圆弧和点连接，形成一个整体结构。构造顺序是从矩形开始，然后添加平行四边形，接着通过线段和圆弧引入新的点，最后将这些点连接成三角形。确保图形保持连贯和对称。
以上提示语为根据原始绘图命令整理而来，仅供参考。