无言证明 by Steve Phelps (3)

无言证明 by Steve Phelps (3)
几何画板及绘图内容加载中,请稍等……
2015-02-18 23:22
这是一个几何作图的无言证明范例。通过拖动点和滑块,观察图形的变化,理解其背后的数学原理。构造了三角形、圆弧、多边形等几何对象,使用了点、交点、向量、变换等GeoGebra命令。适合高中及以上学生或教师使用,帮助理解几何变换和证明方法。

GeoGebra 命令及参数

  1. Point(xAxis) → A
  2. Intersect(xAxis, yAxis) → B
  3. CircleArc(B, D, A) → c
  4. Point(c) → E
  5. Polygon(A, E, 4) → poly1, a, b, d, e, F, G
  6. Polygon(E, C, 4) → poly2, f, g, h, i, H, I
  7. Polygon(C, A, 4) → poly3, j, k, l, m, J, K
  8. AngularBisector(A, E, C) → n
  9. Intersect(n, j) → L
  10. OrthogonalLine(L, a) → p
  11. OrthogonalLine(L, f) → q
  12. Midpoint(G, E) → M
  13. Midpoint(E, H) → N
  14. Intersect(p, a) → O
  15. Intersect(q, f) → P
  16. Mirror(O, M) → O'
  17. Mirror(P, N) → P'
  18. Line(O, j) → r
  19. Line(P, j) → s
  20. Intersect(r, e) → Q
  21. Intersect(s, g) → R
  22. Mirror(Q, M) → Q'
  23. Mirror(R, N) → R'
  24. Polygon(Q, O, 4) → poly4, t, a_1, b_1, c_1, S, T
  25. Polygon(P, R, 4) → poly5, d_1, e_1, f_1, g_1, U, V
  26. Polygon(Q, G, O') → poly6, o', q_1, g_2
  27. Polygon(O', F, Q') → poly7, q', o'_1, f_2
  28. Polygon(Q', O, E) → poly8, e_2, q'_1, o
  29. Polygon(O, A, Q) → poly9, q_2, o_1, a_2
  30. Polygon(E, P, R') → poly10, r', e_3, p_1
  31. Polygon(P, C, R) → poly11, r_1, p_2, c_2
  32. Polygon(R, P', H) → poly12, h_1, r_2, p'
  33. Polygon(I, R', P') → poly13, p'_1, i_1, r'_1
  34. If(0 ≤ u ≤ 1, 1 - u, If[u > 1, 0, 1]) → d1
  35. Dilate(O', d1, A) → O''
  36. Vector(O', O'') → v
  37. Translate(poly4, v) → poly4'
  38. Dilate(R, d1, K) → R'_1
  39. Vector(R, R'_1) → w
  40. Translate(poly5, w) → poly5'
  41. If(1 ≤ u ≤ 2, 2 - u, If[u > 2, 0, 1]) → d2
  42. Dilate(R, d2, J) → R'_2
  43. Vector(R, R'_2) → u_1
  44. Translate(R, u_1) → R'_3
  45. Translate(P', u_1) → P''
  46. Translate(H, u_1) → H'
  47. Polygon(R'_3, P'', H') → poly12', h', r'_3, p''
  48. Dilate(P, d2, W) → P'_1
  49. Vector(P, P'_1) → v_1
  50. Translate(E, v_1) → E'
  51. Translate(P, v_1) → P'_2
  52. Translate(R', v_1) → R''
  53. Polygon(E', P'_2, R'') → poly10', r'', e', p'_2
  54. Dilate(P, d2, L) → P'_3
  55. Vector(P, P'_3) → w_1
  56. Translate(P, w_1) → P'_4
  57. Translate(C, w_1) → C'
  58. Translate(R, w_1) → R'_4
  59. Polygon(P'_4, C', R'_4) → poly11', r'_4, p'_4, c'
  60. Dilate(R', d2, R'') → R''_1
  61. Vector(R', R''_1) → j_1
  62. Translate(I, j_1) → I'
  63. Translate(R', j_1) → R''_2
  64. Translate(P', j_1) → P''_1
  65. Polygon(I', R''_2, P''_1) → poly13', p''_1, i', r''_2
  66. If(2 ≤ u ≤ 3, 3 - u, If[u > 3, 0, 1]) → d3
  67. Dilate(G, d3, C') → G'
  68. Vector(G, G') → k_1
  69. Translate(Q, k_1) → Q'_1
  70. Translate(G, k_1) → G'_1
  71. Translate(O', k_1) → O''_1
  72. Polygon(Q'_1, G'_1, O''_1) → poly6', o''_1, q'_2, g'_1
  73. Dilate(O, d3, R'') → O'_1
  74. Vector(O, O'_1) → l_1
  75. Translate(Q', l_1) → Q''
  76. Translate(O, l_1) → O'_2
  77. Translate(E, l_1) → E'_1
  78. Polygon(Q'', O'_2, E'_1) → poly8', e'_1, q'', o'_2
  79. Dilate(A, d3, H') → A'
  80. Vector(A, A') → m_1
  81. Dilate(F, d3, E') → F'
  82. Vector(F, F') → n_1
  83. Translate(O, m_1) → O'_3
  84. Translate(A, m_1) → A'_1
  85. Translate(Q, m_1) → Q'_2
  86. Polygon(O'_3, A'_1, Q'_2) → poly9', q'_3, o'_3, a'_1
  87. Translate(O', n_1) → O''_2
  88. Translate(F, n_1) → F'_1
  89. Translate(Q', n_1) → Q''_1
  90. Polygon(O''_2, F'_1, Q''_1) → poly7', q''_1, o''_2, f'_1

AI 绘图提示语参考

画一个几何构造图形,包含一个坐标系、点、圆弧、多边形和几何变换。首先在坐标轴上创建点,然后利用这些点构造圆弧和多边形。接着,通过角度平分线和垂线创建新的点和线段。最后,应用镜像和缩放变换,将多边形进行变换并组合,展示几何变换和证明方法。
以上提示语为根据原始绘图命令整理而来,仅供参考。