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无字证明 by Steve Phelps (4)

无字证明 by Steve Phelps (4)
几何画板及绘图内容加载中，请稍等……
2015-12-13 09:03
测试改名0圆几何作图
①本范例通过动态演示证明勾股定理，展示直角三角形三边关系；②涉及核心数学概念：勾股定理、直角三角形、线性方程、圆；③作图要点：使用Point、Mirror、Semicircle、Circle、Polygon、OrthogonalLine、Intersect、Vector、Translate等GeoGebra命令构建图形；④适合高中数学教学或数学爱好者探索几何证明。

GeoGebra 命令及参数

  1. Point(xAxis) → A
  2. Point(yAxis) → B
  3. Mirror(A, B) → A'
  4. Semicircle(A, A') → s
  5. Circle(B, A') → c
  6. Point(s) → C
  7. Polygon(A, C, 4) → poly1, a, b, d, e, D, E
  8. Polygon(C, A', 4) → poly2, f, g, h, i, F, G
  9. Polygon(A', A, 4) → poly3, j, k, l, m, H, I
  10. OrthogonalLine(A', j) → n
  11. OrthogonalLine(C, n) → p
  12. Intersect(n, p) → J
  13. Intersect(n, h) → K
  14. Intersect(p, h) → L
  15. Intersect(n, i) → M
  16. Intersect(p, g) → N
  17. Polygon(C, J, A') → poly4, a', c_1, j_1
  18. Polygon(A', J, N) → poly5, n_1, a'_1, j_2
  19. Polygon(J, K, F, N) → poly6, j_3, k_1, f_1, n_2
  20. Polygon(J, K, G, C) → poly7, j_4, k_2, g_1, c_2
  21. Polygon(C, J, M) → poly8, m_1, c_3, j_5
  22. Polygon(J, M, G, L) → poly9, j_6, m_2, g_2, l_1
  23. Polygon(J, A', F, L) → poly10, j_7, a'_2, f_2, l_2
  24. Vector(J, A') → u
  25. Translate(C, u) → C'
  26. Translate(J, u) → J'
  27. Translate(A', u) → A''
  28. Polygon(C', J', A'') → poly4', a'', c', j'
  29. Vector(J, I) → v
  30. Translate(J, v) → J'_1
  31. Translate(K, v) → K'
  32. Translate(G, v) → G'
  33. Translate(C, v) → C'_1
  34. Polygon(J'_1, K', G', C'_1) → poly7', j'_1, k', g', c'_1
  35. Translate(C, v) → C'_2
  36. Translate(J, v) → J'_2
  37. Translate(M, v) → M'
  38. Polygon(C'_2, J'_2, M') → poly8', m', c'_2, j'_2
  39. Vector(J, A) → w
  40. Translate(A', w) → A''_1
  41. Translate(J, w) → J'_3
  42. Translate(N, w) → N'
  43. Polygon(A''_1, J'_3, N') → poly5', n', a''_1, j'_3
  44. Translate(J, w) → J'_4
  45. Translate(A', w) → A''_2
  46. Translate(F, w) → F'
  47. Translate(L, w) → L'
  48. Polygon(J'_4, A''_2, F', L') → poly10', j'_4, a''_2, f', l'
  49. Vector(J, H) → q
  50. Translate(J, q) → J'_5
  51. Translate(M, q) → M'_1
  52. Translate(G, q) → G'_1
  53. Translate(L, q) → L'_1
  54. Polygon(J'_5, M'_1, G'_1, L'_1) → poly9', j'_5, m'_1, g'_1, l'_1
  55. Translate(J, q) → J'_6
  56. Translate(K, q) → K'_1
  57. Translate(F, q) → F'_1
  58. Translate(N, q) → N'_1
  59. Polygon(J'_6, K'_1, F'_1, N'_1) → poly6', j'_6, k'_1, f'_1, n'_1
  60. Polygon(A, E, D, C) → poly11, a_1, e_1, d_1, c_4
  61. Vector(D, C') → r
  62. Translate(A, r) → A'_1
  63. Translate(E, r) → E'
  64. Translate(D, r) → D'
  65. Translate(C, r) → C'_3
  66. Polygon(A'_1, E', D', C'_3) → poly11', a'_3, e', d', c'_3