缺失正方形分割

缺失正方形分割
几何画板及绘图内容加载中,请稍等……
2013-04-22 04:35
①这个范例演示了一个看似完美拼接但出现面积缺失的几何图形现象;②涉及的核心数学概念包括几何拼接、面积守恒、旋转变换;③作图要点——从下方『构造摘要』提炼用到了Intersect(交点)、Point(点)、Polygon(多边形)、Midpoint(中点)、OrthogonalLine(垂线)、Rotate(旋转)、Circle(圆)、Segment(线段)、LineBisector(角平分线)等GeoGebra命令/对象;④适合高中数学教学,用于探讨几何变换与面积不变性。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → A
  2. Point(xAxis) → B
  3. Polygon(A, B, 4) → poly1, a_1, b_2, c_3, d_3, C, D
  4. Midpoint(D, B) → E
  5. OrthogonalLine(E, xAxis) → e_5
  6. Rotate(e_5, a, E) → e'
  7. Intersect(e', a_1) → H
  8. OrthogonalLine(E, e') → f
  9. Intersect(f, b_2) → I
  10. Polygon(H, B, I, E) → poly3, h_1, b_1, i, e_2
  11. Intersect(f, d_3) → G
  12. Polygon(A, H, E, G) → poly2, a_2, h, e_1, g
  13. Circle(A, e_1) → p
  14. Intersect(p, a_2, 1) → J
  15. Circle(J, e_2) → r
  16. Intersect(r, xAxis, 2) → L
  17. Circle(L, (2 * e_2)) → k_1
  18. OrthogonalLine(L, xAxis) → j_1
  19. Intersect(k_1, j_1, 2) → N
  20. OrthogonalLine(N, j_1) → l_1
  21. Intersect(l_1, yAxis) → O
  22. Segment(E, O) → s_1
  23. LineBisector(s_1) → c_2
  24. Circle(O, e_2) → p_1
  25. Intersect(p_1, l_1, 1) → P
  26. Segment(G, P) → t_1
  27. LineBisector(t_1) → d_2
  28. Intersect(c_2, d_2) → R
  29. Segment(E, N) → m_1
  30. LineBisector(m_1) → r_1
  31. Segment(I, P) → n_1
  32. LineBisector(n_1) → q_1
  33. Intersect(q_1, r_1) → Q
  34. Segment(E, L) → s
  35. LineBisector(s) → t
  36. Segment(I, J) → n
  37. LineBisector(n) → q
  38. Intersect(q, t) → M
  39. Intersect(e', c_3) → F
  40. Polygon(I, C, F, E) → poly4, i_1, c_1, f_1, e_3
  41. Polygon(F, D, G, E) → poly5, f_2, d_1, g_1, e_4
  42. Segment(A, E) → j
  43. LineBisector(j) → k
  44. Segment(G, J) → l
  45. LineBisector(l) → m
  46. Intersect(k, m) → K
  47. Rotate(A, b, K) → A'
  48. Rotate(H, b, K) → H'
  49. Rotate(E, b, K) → E'
  50. Rotate(G, b, K) → G'
  51. Polygon(A', H', E', G') → poly2', a', h', e'_1, g'
  52. Rotate(B, c, M) → B'
  53. Rotate(I, c, M) → I'
  54. Rotate(E, c, M) → E'_1
  55. Rotate(H, c, M) → H'_1
  56. Polygon(H'_1, B', I', E'_1) → poly3', h'_1, b', i', e'_2
  57. Rotate(C, d, Q) → C'
  58. Rotate(F, d, Q) → F'
  59. Rotate(E, d, Q) → E'_2
  60. Rotate(I, d, Q) → I'_1
  61. Polygon(I'_1, C', F', E'_2) → poly4', i'_1, c', f', e'_3
  62. Rotate(F, e, R) → F'_1
  63. Rotate(G, e, R) → G'_1
  64. Rotate(E, e, R) → E'_3
  65. Rotate(D, e, R) → D'
  66. Polygon(F'_1, D', G'_1, E'_3) → poly5', f'_1, d', g'_1, e'_4

AI 绘图提示语参考

画一个看似完美的正方形,将其分割成几块,重新排列后会发现面积缺失。展示关键几何变换,如旋转和对称,强调面积守恒。先画出正方形和坐标轴,再通过旋转、中点和垂线构造出几块不规则图形,最后将它们重新组合,突出缺失的面积。
以上提示语为根据原始绘图命令整理而来,仅供参考。