正多边形与面积

正多边形与面积
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2016-05-13 03:10
该GeoGebra范例展示了正多边形及其内切圆半径、外接圆半径和面积的计算。通过构造正多边形、中点、线段、角平分线、交点、角度和面积等,学生可以直观理解正多边形的性质及其面积计算方法。适合初中及以上学生学习几何与面积计算。

GeoGebra 命令及参数

  1. Polygon(A, B, 5) → poly3, l, m, n, p, f_2, F, G, H
  2. Midpoint(f_2) → S_1
  3. Segment(S_1, F) → p_3
  4. Midpoint(m) → R_1
  5. Segment(R_1, H) → n_3
  6. Segment(A, B) → a
  7. Polygon(A, B, 3) → poly1, b, c, d, C
  8. Polygon(A, B, 4) → poly2, f, g, h, i, D, E
  9. Polygon(A, B, 6) → poly4, q, L, r, s, t, a_1, b_1, I, J, K
  10. Midpoint(a) → M
  11. AngularBisector(C, B, A) → c_1
  12. AngularBisector(B, A, C) → d_1
  13. AngularBisector(A, C, B) → e_1
  14. Intersect(e_1, d_1) → N
  15. Segment(N, B) → f_1
  16. Segment(N, A) → g_1
  17. Segment(N, C) → h_1
  18. Midpoint(d) → O
  19. Midpoint(c) → P
  20. Segment(N, P) → i_1
  21. Segment(N, O) → j_1
  22. Segment(M, N) → k_1
  23. Midpoint(a) → Q
  24. Midpoint(i) → R
  25. Midpoint(h) → S
  26. Midpoint(g) → T
  27. AngularBisector(E, D, B) → l_1
  28. AngularBisector(D, B, A) → m_1
  29. Intersect(l_1, m_1) → U
  30. Midpoint(h) → V
  31. Midpoint(i) → W
  32. Midpoint(g) → Z
  33. Midpoint(a) → A_1
  34. Segment(U, Z) → n_1
  35. Segment(U, V) → p_1
  36. Segment(U, W) → q_1
  37. Segment(U, A_1) → r_1
  38. Segment(U, B) → s_1
  39. Segment(U, D) → t_1
  40. Segment(U, E) → a_2
  41. Segment(U, A) → b_2
  42. Angle(M, N, B) → α
  43. Angle(N, B, A) → β
  44. Angle(a, k_1) → γ
  45. Angle(A_1, U, B) → δ
  46. Angle(U, B, A) → ε
  47. Intersect(r_1, a) → B_1
  48. Angle(B, B_1, U) → ζ
  49. Midpoint(a) → F_1
  50. Midpoint(a_1) → K_1
  51. Midpoint(b_1) → L_1
  52. Midpoint(a) → M_1
  53. Midpoint(r) → N_1
  54. Midpoint(s) → O_1
  55. Midpoint(t) → P_1
  56. AngularBisector(K, J, I) → p_2
  57. AngularBisector(J, I, B) → q_2
  58. Intersect(q_2, p_2) → Q_1
  59. Segment(Q_1, I) → r_2
  60. Segment(N_1, Q_1) → s_2
  61. Segment(Q_1, B) → t_2
  62. Segment(M_1, Q_1) → a_3
  63. Segment(Q_1, O_1) → c_3
  64. Segment(J, Q_1) → d_3
  65. Segment(Q_1, P_1) → e_3
  66. Segment(K, Q_1) → f_3
  67. Segment(Q_1, K_1) → g_3
  68. Segment(L, Q_1) → h_3
  69. Segment(Q_1, L_1) → i_3
  70. Angle(M_1, Q_1, B) → κ
  71. Angle(Q_1, B, M_1) → λ
  72. Angle(B, M_1, Q_1) → μ
  73. Segment(A, Q_1) → k
  74. Midpoint(f_2) → C_1
  75. Midpoint(p) → D_1
  76. Midpoint(n) → E_1
  77. Midpoint(m) → G_1
  78. Midpoint(b) → H_1
  79. Segment(H_1, G) → g_2
  80. Segment(F, C_1) → h_2
  81. Intersect(n_3, p_3) → I_1
  82. Segment(H_1, I_1) → i_2
  83. Segment(I_1, G_1) → j_2
  84. Segment(I_1, E_1) → k_2
  85. Segment(I_1, D_1) → l_2
  86. Segment(I_1, C_1) → m_2
  87. Segment(G, I_1) → n_2
  88. Segment(I_1, F) → c_2
  89. Segment(B, I_1) → d_2
  90. Segment(A, I_1) → e_2
  91. Segment(H, I_1) → j_3
  92. Angle(B, Q, I_1) → η
  93. Angle(Q, I_1, B) → θ
  94. Angle(I_1, B, Q) → ι
  95. Midpoint(b) → J_1
  96. Polygon(B, A, N) → poly5, k_3, l_3, m_3
  97. Area(poly5) → u_1
  98. Perimeter(poly1) → v_1
  99. Polygon(A, U, B) → poly6, b_3, a_4, u_2
  100. Perimeter(poly6) → o_2
  101. Polygon(A, I_1, B) → poly7, b_4, a_5, i_4
  102. Perimeter(poly3) → v_2
  103. Polygon(A, Q_1, B) → poly8, b_5, a_6, q_3
  104. Perimeter(poly4) → w_2

AI 绘图提示语参考

画一个正五边形,并标出其边的中点和连接中点与顶点的线段。再画一个正三角形和一个正方形,同样标出边的中点和连接中点与顶点的线段。接着,画一个正六边形,并标出其边的中点和连接中点与顶点的线段。最后,画三个角平分线,交于一点,并从交点向正三角形的顶点画三条线段。
以上提示语为根据原始绘图命令整理而来,仅供参考。