勾股定理探索 by Veronika Havelková

勾股定理探索 by Veronika Havelková
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2014-11-09 22:22
①本范例通过移动点演示直角三角形三边关系;②涉及核心数学概念为勾股定理、直角三角形、坐标几何;③作图要点:使用Point, Semicircle, Midpoint, OrthogonalLine, Intersect, Circle, CircleArc, Polygon, Segment等GeoGebra命令构建图形;④适合初中及以上学生学习和理解勾股定理的证明及应用。

GeoGebra 命令及参数

  1. Point(xAxis) → A
  2. Point(xAxis) → B
  3. Semicircle(A, B) → c
  4. Midpoint(A, B) → C
  5. OrthogonalLine(C, xAxis) → a
  6. Intersect(c, a) → D,
  7. Circle(D, 0.1) → d
  8. Intersect(d, c) → E, F, ,
  9. CircleArc(C, F, A) → e
  10. Point(e) → G
  11. Polygon(A, B, G) → mnohoúhelník1, g, a_1, b
  12. Polygon(G, B, 4) → mnohoúhelník2, f, h, i, j, H, I
  13. Polygon(A, G, 4) → mnohoúhelník3, k, l, m, n, J, K
  14. Polygon(B, A, 4) → mnohoúhelník4, p, q, r, s, L, M
  15. Segment(G, H) → t
  16. Segment(B, I) → b_1
  17. Intersect(t, b_1) → N
  18. OrthogonalLine(N, g) → c_1
  19. OrthogonalLine(N, c_1) → d_1
  20. Intersect(d_1, j) → O
  21. Intersect(d_1, h) → P
  22. Intersect(f, c_1) → Q
  23. Intersect(c_1, i) → R
  24. Segment(Q, B) → e_1
  25. Segment(B, H) → f_1
  26. Segment(H, I) → g_1
  27. Segment(I, G) → h_1
  28. Segment(G, Q) → i_1
  29. Segment(Q, N) → j_1
  30. Segment(N, P) → k_1
  31. Segment(N, R) → l_1
  32. Segment(N, O) → m_1
  33. Circle(L, Segment[N, P]) → p_1
  34. Circle(M, Segment[N, Q]) → q_1
  35. Circle(B, Segment[N, Q]) → r_1
  36. Circle(A, Segment[N, Q]) → s_1
  37. Intersect(p_1, r) → S,
  38. Intersect(q_1, s) → T,
  39. Intersect(r_1, g) → U,
  40. Intersect(s_1, q) → V,
  41. Circle(Q, Segment[B, Q]) → t_1
  42. Circle(S, Segment[Q, B]) → c_2
  43. Circle(T, Segment[Q, B]) → d_2
  44. Circle(U, Segment[B, Q]) → e_2
  45. Circle(V, Segment[Q, B]) → f_2
  46. Intersect(t_1, j_1) → W,
  47. Intersect(c_2, r) → Z, A_1
  48. Intersect(d_2, s) → B_1, C_1
  49. Intersect(g, p) → D_1
  50. Intersect(e_2, g) → E_1, F_1
  51. Intersect(e_2, f_2) → G_1, N_1, ,
  52. Intersect(f_2, q) → H_1, I_1
  53. Circle(Z, Segment[B, W]) → g_2
  54. Circle(B_1, Segment[B, W]) → h_2
  55. Circle(F_1, Segment[B, W]) → k_2
  56. Circle(H_1, Segment[B, W]) → p_2
  57. Intersect(c_2, g_2, 2) → J_1
  58. Intersect(d_2, h_2, 2) → K_1
  59. Intersect(e_2, k_2, 2) → L_1
  60. Intersect(f_2, p_2, 2) → M_1
  61. Segment(L, S) → n_1
  62. Segment(S, J_1) → a_2
  63. Segment(J_1, V) → b_2
  64. Segment(V, L) → i_2
  65. Segment(S, M) → j_2
  66. Segment(M, B) → l_2
  67. Segment(B, A) → m_2
  68. Segment(A, L) → n_2
  69. Segment(S, K_1) → q_2
  70. Segment(T, L_1) → r_2
  71. Segment(U, M_1) → s_2
  72. Polygon(L, S, J_1, V) → mnohoúhelník5, l_3, s_3, j_3, v
  73. Polygon(S, M, T, K_1) → mnohoúhelník6, s_4, m_3, t_2, k_3
  74. Polygon(T, B, U, L_1) → mnohoúhelník7, t_3, b_3, u, l_4
  75. Polygon(U, A, V, M_1) → mnohoúhelník8, u_1, a_3, v_1, m_4
  76. Polygon(Q, B, P, N) → mnohoúhelník9, q_3, b_4, p_3, n_3
  77. Polygon(Q, G, O, N) → mnohoúhelník10, q_4, g_3, o, n_4
  78. Polygon(N, P, H, R) → mnohoúhelník11, n_5, p_4, h_3, r_3
  79. Polygon(N, O, I, R) → mnohoúhelník12, n_6, o_1, i_3, r_4
  80. Polygon(M_1, J_1, K_1, L_1) → mnohoúhelník13, m_5, j_4, k_4, l_5
  81. Polygon(A, B, G) → mnohoúhelník14, g_4, a_4, b_5
  82. Segment(A, K) → c_3
  83. Segment(K, J) → d_3
  84. Segment(J, G) → e_3
  85. Segment(G, A) → f_3
  86. Segment(L, M) → c_4

AI 绘图提示语参考

在坐标平面上,先画一条水平线段作为直角三角形的一条边,并以其为直径作一个半圆。在半圆上取一点,连接该点与线段两端点,构成一个直角三角形。接着,以该直角三角形的三条边为边,分别向外作正方形。然后,在图形内部添加辅助线段和交点,构造出若干小三角形和四边形,以展示勾股定理的几何证明。最后,在关键位置绘制一些圆,用于标记或辅助说明。整体图形应清晰展示直角三角形三边上的正方形面积关系。
以上提示语为根据原始绘图命令整理而来,仅供参考。