无言证明 by Steve Phelps (7)

无言证明 by Steve Phelps (7)
几何画板及绘图内容加载中,请稍等……
2015-02-15 09:25
通过拖动点和滑块,观察图形的变化,探索勾股定理的证明。本例使用了点、圆弧、多边形、向量等 GeoGebra 命令,展示了动态几何的魅力。适合初中及以上学生学习几何证明。

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. Polygon(A, E, F) → poly4, f_1, a_1, e_1
  9. Polygon(E, C, H) → poly5, h_1, e_2, c_1
  10. Polygon(C, A, J) → poly6, j_1, c_2, a_2
  11. OrthogonalLine(C, j_1) → n
  12. Intersect(n, c_1) → L
  13. Polygon(E, L, C) → poly7, c_3, e_3, l_1
  14. Midpoint(j_1) → M
  15. If(o ≤ 1, o, If[1 < o, 1, 0]) → r1
  16. Rotate(E, (-(((r1 * 180))°)), M) → E'
  17. Rotate(L, (-(((r1 * 180))°)), M) → L'
  18. Rotate(C, (-(((r1 * 180))°)), M) → C'
  19. Polygon(E', L', C') → poly7', c', e', l'
  20. Polygon(C, L, H) → poly8, h_2, c_4, l_2
  21. If(1 ≤ o ≤ 2, 2 - o, If[2 < o, 0, 1]) → d1
  22. Dilate(C, d1, A) → C'_1
  23. Vector(C, C'_1) → u
  24. Translate(C, u) → C'_2
  25. Translate(L, u) → L'_1
  26. Translate(H, u) → H'
  27. Polygon(C'_2, L'_1, H') → poly8', h', c'_2, l'_1
  28. If(1 ≤ o ≤ 2, o - 1, If[2 < o, 1, 0]) → r2
  29. Rotate(C'_2, (-(((r2 * 90))°)), C'_2) → N
  30. Rotate(L'_1, (-(((r2 * 90))°)), C'_2) → O
  31. Rotate(H', (-(((r2 * 90))°)), C'_2) → H''
  32. Polygon(N, O, H'') → poly8'', h'', n_1, o_1
  33. OrthogonalLine(E, n) → p
  34. Intersect(p, e_1) → P
  35. Polygon(P, A, E) → poly9, e_4, p_1, a_3
  36. If(2 ≤ o ≤ 3, 3 - o, If[3 < o, 0, 1]) → d2
  37. Dilate(E, d2, C) → E'_1
  38. Vector(E, E'_1) → v
  39. Translate(P, v) → P'
  40. Translate(A, v) → A'
  41. Translate(E, v) → E'_2
  42. Polygon(P', A', E'_2) → poly9', e'_2, p', a'
  43. Polygon(P, F, E) → poly10, e_5, p_2, f_2
  44. If(3 ≤ o ≤ 4, 4 - o, If[4 < o, 0, 1]) → d3
  45. Dilate(E, d3, J) → E'_3
  46. Vector(E, E'_3) → w
  47. Translate(P, w) → P'_1
  48. Translate(F, w) → F'
  49. Translate(E, w) → E'_4
  50. Polygon(P'_1, F', E'_4) → poly10', e'_4, p'_1, f'
  51. If(3 ≤ o ≤ 4, o - 3, If[4 < o, 1, 0]) → r3
  52. Rotate(P'_1, (-(((r3 * 90))°)), E'_3) → Q
  53. Rotate(F', (-(((r3 * 90))°)), E'_3) → F''
  54. Rotate(E'_4, (-(((r3 * 90))°)), E'_3) → R
  55. Polygon(Q, F'', R) → poly10'', r, q, f''
  56. Intersect(a_2, c') → S
  57. Polygon(S, C, H'') → poly11, h''_1, s, c_5
  58. If(4 ≤ o ≤ 5, o - 4, If[5 < o, 1, 0]) → r4
  59. Rotate(S, (-(((r4 * 180))°)), S) → S'
  60. Rotate(C, (-(((r4 * 180))°)), S) → C'_3
  61. Rotate(H'', (-(((r4 * 180))°)), S) → H'''
  62. Polygon(S', C'_3, H''') → poly11', h''', s', c'_3

AI 绘图提示语参考

画一个直角三角形,用圆弧和正方形展示勾股定理。首先标出坐标轴上的点和交点,然后画出圆弧和三个正方形,分别位于三角形的三条边上。通过动态调整这些图形的位置和大小,观察它们之间的关系,直观证明勾股定理。
以上提示语为根据原始绘图命令整理而来,仅供参考。