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圆内接正多边形

圆内接正多边形
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2016-04-15 04:20
测试改名0圆多边形几何作图
① 本范例演示如何在给定圆内构造正多边形（如正三角形、正方形等），并展示其内接于圆的性质。② 核心数学概念包括正多边形的定义、圆内接多边形的顶点共圆、等边三角形与正多边形的几何关系，以及圆与多边形的对称性。③ 作图要点：从构造摘要可见，使用了GeoGebra的Circle（圆）、Line（直线）、OrthogonalLine（垂线）、Intersect（交点）、Segment（线段）、CircleArc（圆弧）等命令，创建了对象A、B、c、C、D等，通过构造辅助线和交点来确定正多边形的顶点，并利用圆弧和线段连接形成正多边形。④ 适合中学几何课程，用于直观理解正多边形的内接性质、尺规作图原理，以及圆与多边形的关系，也可用于数学实验和动态探索。

GeoGebra 命令及参数

  1. Circle(A, B) → c
  2. Circle(C, D) → d
  3. Line(A, xAxis) → a
  4. OrthogonalLine(A, a) → b
  5. Intersect(c, b, 2) → E
  6. Intersect(c, b, 1) → F
  7. Segment(E, F) → e
  8. Circle(F, A) → f
  9. Intersect(c, f, 2) → G
  10. Intersect(c, f, 1) → H
  11. CircleArc(F, H, G) → g
  12. Segment(E, H) → h
  13. Segment(H, G) → i
  14. Segment(G, E) → j
  15. Circle(E, A) → p
  16. Intersect(c, p, 1) → I
  17. Intersect(c, p, 2) → J
  18. CircleArc(E, I, J) → q
  19. Segment(E, J) → l
  20. Segment(J, H) → m
  21. Segment(H, F) → n
  22. Segment(F, G) → r
  23. Segment(G, I) → s
  24. Segment(I, E) → t
  25. Intersect(c, a, 1) → K
  26. Intersect(c, a, 2) → L
  27. Circle(K, A) → c_1
  28. Circle(L, A) → d_1
  29. Intersect(c, c_1, 2) → M
  30. Intersect(c, c_1, 1) → N
  31. Intersect(c, d_1, 1) → O
  32. Intersect(c, d_1, 2) → P
  33. CircleArc(K, N, M) → e_1
  34. CircleArc(L, O, P) → f_1
  35. Segment(E, O) → a_1
  36. Segment(O, J) → b_1
  37. Segment(J, L) → g_1
  38. Segment(L, H) → h_1
  39. Segment(H, P) → i_1
  40. Segment(P, F) → j_1
  41. Segment(F, N) → k_1
  42. Segment(N, G) → l_1
  43. Segment(G, K) → m_1
  44. Segment(K, I) → n_1
  45. Segment(I, M) → p_1
  46. Segment(M, E) → q_1
  47. Segment(K, L) → r_1
  48. OrthogonalLine(C, a) → s_1
  49. Intersect(d, s_1) → Q, R
  50. Intersect(d, a) → S, T
  51. Circle(S, 3) → t_1
  52. Circle(R, 3) → c_2
  53. Intersect(t_1, c_2, 1) → U
  54. Circle(T, 3) → d_2
  55. Intersect(c_2, d_2, 1) → V
  56. Circle(U, 0.5) → e_2
  57. Circle(V, 0.5) → f_2
  58. Intersect(c_2, f_2, 1) → W
  59. Intersect(d_2, f_2, 2) → Z
  60. Intersect(c_2, f_2, 2) → A_1
  61. Intersect(d_2, f_2, 1) → B_1
  62. Intersect(c_2, e_2, 2) → C_1
  63. Intersect(t_1, e_2, 1) → D_1
  64. Intersect(c_2, e_2, 1) → E_1
  65. Intersect(t_1, e_2, 2) → F_1
  66. CircleArc(T, Z, B_1) → g_2
  67. CircleArc(R, A_1, W) → h_2
  68. CircleArc(R, C_1, E_1) → k_2
  69. CircleArc(S, F_1, D_1) → p_2
  70. Intersect(g_2, h_2, 1) → G_1
  71. Line(U, C) → a_2
  72. Line(G_1, C) → b_2
  73. Intersect(d, b_2, 2) → H_1
  74. Intersect(d, a_2, 2) → I_1
  75. Intersect(e_2, a_2, 1) → J_1
  76. Intersect(f_2, b_2, 1) → K_1
  77. Segment(J_1, I_1) → i_2
  78. Segment(G_1, H_1) → j_2
  79. Segment(R, Q) → l_2
  80. Segment(S, T) → m_2
  81. Intersect(a_2, i_2) → L_1
  82. Intersect(a_2, i_2) → M_1
  83. Intersect(a_2, i_2) → N_1
  84. Intersect(a_2, i_2) → O_1
  85. Intersect(d, a_2, 1) → P_1
  86. Intersect(d, b_2, 1) → Q_1
  87. Segment(P_1, Q_1) → n_2
  88. Segment(Q_1, I_1) → q_2
  89. Segment(I_1, H_1) → r_2
  90. Segment(H_1, P_1) → s_2
  91. Segment(R, Q_1) → t_2
  92. Segment(Q_1, T) → a_3
  93. Segment(T, I_1) → b_3
  94. Segment(I_1, Q) → c_3
  95. Segment(Q, H_1) → d_3
  96. Segment(H_1, S) → e_3
  97. Segment(S, P_1) → f_3
  98. Segment(P_1, R) → g_3
  99. Intersect(g_2, h_2, 1) → R_1
  100. Line(C, R_1) → h_3
  101. Intersect(f_2, h_3, 2) → S_1
  102. Intersect(d, h_3, 1) → T_1
  103. Segment(S_1, T_1) → i_3