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制作正方形

制作正方形
几何画板及绘图内容加载中，请稍等……
2017-01-20 09:04
角变换几何作图
这个范例演示了如何使用GeoGebra制作正方形。涉及的核心数学概念包括几何作图、角度和变换。通过使用Circle, Intersect, Polygon, Segment, Rotate, Line, Point, Angle, Sequence, AngularBisector等命令，可以构建出正方形。适合初中及以上学生学习几何作图和变换。

GeoGebra 命令及参数

  1. Circle(G, leg1) → c
  2. Intersect(c, f, 2) → B'
  3. Circle(G, leg2) → d
  4. Intersect(d, g, 1) → C'
  5. Circle(C', leg2) → e
  6. Polygon(G, B', C') → polyG, c', a', b'
  7. Circle(F, leg2) → k
  8. Intersect(k, m) → B_2, C_1
  9. Intersect(n, p) → D_2
  10. Circle(D_2, leg2 - leg1) → r
  11. Intersect(r, p, 1) → E_2
  12. Circle(D_2, leg1) → s
  13. Intersect(s, n, 1) → F_2
  14. Intersect(q, p) → G_1
  15. Segment(F, E_2) → t_3
  16. Rotate(F, (-(90°)), E_2) → A'_1
  17. Line(E_2, A'_1) → a
  18. Intersect(n, a) → H_1
  19. Polygon(F, C_1, H_1, E_2) → polyF, a_1, c_1, h_1, e_1
  20. Circle(E, leg1) → d_1
  21. Intersect(d_1, b, 2) → J
  22. Circle(E, leg1^(2) / leg2) → k_1
  23. Intersect(k_1, g_1, 2) → K
  24. Polygon(E, J, K) → polyE, k_2, i_1, j_1
  25. Circle(H, leg1) → t_1
  26. Intersect(t_1, r_1, 2) → P
  27. Circle(H, leg1 - leg1^(2) / leg2) → c_2
  28. Intersect(c_2, s_1, 1) → Q
  29. Intersect(b_1, f_2) → R
  30. Polygon(H, P, R, Q) → polyH, o, p_2, r_2, q_2
  31. Circle(D, leg2 - leg1) → d_2
  32. Intersect(d_2, g_2, 2) → T
  33. Circle(T, leg1 - leg1^(2) / leg2) → e_2
  34. Intersect(e_2, h_2, 1) → U
  35. Polygon(D, T, U) → polyD, u_1, s_2, t_2
  36. Point(Circle[B, leg2]) → M
  37. Segment(B, M) → l_1
  38. Polygon(B, M, 4) → polyB, m_1, n_1, p_1, q_1, N, V
  39. Point(Circle[A, leg1]) → Z
  40. Segment(A, Z) → i_2
  41. Polygon(A, Z, 4) → polyA, j_2, l_2, m_2, n_2, A_1, B_1
  42. Point(Circle[C, sqrt(leg1^(2) + leg2^(2))]) → D_1
  43. Segment(C, D_1) → a_2
  44. Polygon(C, D_1, 4) → polyC, b_2, f_3, g_3, h_3, E_1, F_1
  45. Angle(polyG) → α, β, γ
  46. Sequence(Segment[(x(B), y(B) + w), (x(B) + leg2, y(B) + w)], w, 0, leg2) → list2
  47. Sequence(Segment[(x(B) + w, y(B)), (x(B) + w, y(B) + leg2)], w, 0, leg2) → list5
  48. Sequence(Segment[(x(A), y(A) + w), (x(A) + leg1, y(A) + w)], w, 0, leg1) → list3
  49. Sequence(Segment[(x(A) + w, y(A)), (x(A) + w, y(A) + leg1)], w, 0, leg1) → list6
  50. Sequence(Segment[(x(C), y(C) + w), (x(C) + hyp, y(C) + w)], w, 0, hyp) → list1
  51. Sequence(Segment[(x(C) + w, y(C)), (x(C) + w, y(C) + hyp)], w, 0, hyp) → list4
  52. Rotate(polyC, ε, C) → polyC'
  53. Rotate(list1, ε, C) → list1'
  54. Rotate(list4, ε, C) → list4'
  55. AngularBisector(F, C_1, H_1) → i_3
  56. AngularBisector(F, E_2, C_1) → j_3
  57. Intersect(i_3, j_3) → I
  58. AngularBisector(E, J, K) → k_3
  59. AngularBisector(K, E, J) → l_3
  60. AngularBisector(J, K, E) → m_3
  61. Intersect(k_3, l_3) → L
  62. AngularBisector(C', G, B') → n_3
  63. AngularBisector(B', C', G) → p_3
  64. Intersect(n_3, p_3) → O
  65. AngularBisector(P, H, Q) → q_3
  66. AngularBisector(H, P, R) → r_3
  67. AngularBisector(H, Q, R) → s_3
  68. AngularBisector(Q, R, P) → a_3
  69. Intersect(r_3, a_3) → S
  70. AngularBisector(D, T, U) → b_3
  71. AngularBisector(U, D, T) → c_3
  72. Intersect(b_3, c_3) → W