无字证明 by Steve Phelps (7)

无字证明 by Steve Phelps (7)
几何画板及绘图内容加载中,请稍等……
2015-02-04 03:56
①本范例通过拖动点演示三角形与平行四边形的几何关系;②涉及核心概念:交点、平面图形、数列、方差、最小公倍数与最大公约数;③作图要点:使用Point, Intersect, Mirror, Segment, OrthogonalLine, Polygon, CircleArc, PointIn, Vector, Centroid, Translate, Midpoint等命令构建图形;④适合高中及以上学生及数学爱好者用于探索几何证明与变换。

GeoGebra 命令及参数

  1. Point(xAxis) → A
  2. Intersect(xAxis, yAxis) → B
  3. Mirror(A, B) → A'
  4. Segment(A, A') → h_1
  5. OrthogonalLine(A', h_1) → j_1
  6. Polygon(A', A, 4) → poly2, f, g, h, i, G, H
  7. CircleArc(B, C, A) → c
  8. Point(c) → D
  9. Polygon(D, A', 4) → poly1, a, b, d, e, E, F
  10. OrthogonalLine(E, j_1) → p_1
  11. Intersect(j_1, p_1) → D_1
  12. OrthogonalLine(F, h_1) → i_1
  13. Intersect(i_1, p_1) → A_1
  14. OrthogonalLine(D, i_1) → q_1
  15. Intersect(j_1, q_1) → E_1
  16. Intersect(i_1, q_1) → F_1
  17. Polygon(F_1, A_1, D_1, E_1) → poly9, f_3, a_2, d_3, e_3
  18. PointIn(poly9) → K
  19. Vector(K, G) → v
  20. OrthogonalLine(K, f) → n
  21. Intersect(n, poly1) → N, O
  22. OrthogonalLine(K, n) → p
  23. Intersect(p, poly1) → L, M
  24. Polygon(K, N, F, E, M) → poly4, k_1, n_1, f_1, e_1, m_1
  25. Centroid(poly4) → P
  26. Translate(P, v) → P'
  27. Vector(P, P') → s_1
  28. Translate(E, s_1) → E'_2
  29. Polygon(A, D, 4) → poly3, j, k, l, m, I, J
  30. Midpoint(I, A) → Z
  31. Polygon(O, K, M, E, A') → poly7, o_1, k_4, m_2, e_2, a'_1
  32. Centroid(poly7) → S
  33. Vector(K, A) → u
  34. Translate(S, u) → S'
  35. Segment(S, S') → s
  36. Point(s) → U
  37. Vector(S, U) → v_1
  38. Translate(A', v_1) → A''
  39. Vector(A, E'_2) → r_1
  40. Translate(Z, r_1) → Z'
  41. Vector(K, H) → q
  42. Vector(K, A') → w
  43. Polygon(L, D, A', O, K) → poly6, l_2, d_2, a', o, k_3
  44. Centroid(poly6) → R
  45. Translate(R, w) → R'
  46. Polygon(L, D, F, N, K) → poly5, l_1, d_1, f_2, n_2, k_2
  47. Centroid(poly5) → Q
  48. Translate(Q, q) → Q'
  49. Polygon(S', R', Q', P') → poly8, s', r', q', p'
  50. Centroid(poly8) → C_1
  51. Segment(Q, Q') → r
  52. Segment(R, R') → t
  53. Segment(P, P') → a_1
  54. Point(a_1) → T
  55. Vector(P, T) → u_1
  56. Point(t) → V
  57. Vector(R, V) → w_1
  58. Point(r) → W
  59. Vector(Q, W) → b_1
  60. Translate(L, b_1) → L'
  61. Translate(D, b_1) → D'
  62. Translate(F, b_1) → F'
  63. Translate(N, b_1) → N'
  64. Translate(K, b_1) → K'
  65. Polygon(L', D', F', N', K') → poly5', l', d', f', n', k'
  66. Translate(K, u_1) → K'_1
  67. Translate(N, u_1) → N'_1
  68. Translate(F, u_1) → F'_1
  69. Translate(E, u_1) → E'
  70. Translate(M, u_1) → M'
  71. Polygon(K'_1, N'_1, F'_1, E', M') → poly4', k'_1, n'_1, f'_1, e', m'
  72. Translate(O, v_1) → O'
  73. Translate(K, v_1) → K'_2
  74. Translate(M, v_1) → M'_1
  75. Translate(E, v_1) → E'_1
  76. Polygon(O', K'_2, M'_1, E'_1, A'') → poly7', o', k'_2, m'_1, e'_1, a''
  77. Translate(L, w_1) → L'_1
  78. Translate(D, w_1) → D'_1
  79. Translate(A', w_1) → A''_1
  80. Translate(O, w_1) → O'_1
  81. Translate(K, w_1) → K'_3
  82. Polygon(L'_1, D'_1, A''_1, O'_1, K'_3) → poly6', l'_1, d'_1, a''_1, o'_1, k'_3
  83. Segment(Z, Z') → c_1
  84. Point(c_1) → B_1
  85. Vector(Z, B_1) → g_1
  86. Translate(poly3, g_1) → poly3'

AI 绘图提示语参考

画一个几何图形,展示三角形与平行四边形的几何关系。通过拖动点观察变化,核心包含交点、平面图形、数字、变异数、最小公倍数和最大公约数。先画坐标轴交点,镜像生成对称点,连接形成平行四边形和四边形,再利用圆弧交点构造新图形,通过正交线、中点和重心进行平移变换,最终形成多个嵌套的多边形和连接线,体现几何变换与证明。
以上提示语为根据原始绘图命令整理而来,仅供参考。