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埃加多·阿兰德特的勾股定理证明 #4

埃加多·阿兰德特的勾股定理证明 #4
几何画板及绘图内容加载中，请稍等……
2012-11-18 07:19
测试改名0角解析几何几何作图
这个范例展示了埃加多·阿兰德特提出的勾股定理证明，通过动态几何方式演示了直角三角形的边与斜边之间的关系。核心数学概念包括勾股定理、三角形性质及坐标几何。作图中使用了 GeoGebra 的 Segment、Point、Polygon 和 Intersect 命令，构建了多个点和线段，通过交点验证了 a² + b² = c² 的等式。该范例适合高中几何教学及数学竞赛备考使用。

GeoGebra 命令及参数

  1. Segment(A, B) → a
  2. Segment(A, C) → b
  3. Segment(C, D) → c
  4. Segment(D, B) → d
  5. Segment(A, E) → e
  6. Segment(E, B) → f
  7. Segment(E, F) → g
  8. Segment(A, G) → h
  9. Segment(G, F) → i
  10. Segment(E, H) → j
  11. Segment(H, I) → k
  12. Segment(I, J) → l
  13. Segment(J, K) → m
  14. Segment(K, B) → n
  15. Segment(L, M) → p
  16. Segment(A, L) → q
  17. Segment(M, C) → r
  18. Segment(N, O) → s
  19. Segment(N, B) → t
  20. Segment(O, D) → a_1
  21. Point(f) → P
  22. Segment(P, Q) → b_1
  23. Segment(Q, A) → c_1
  24. Segment(N, R) → d_1
  25. Segment(M, S) → e_1
  26. Point(e_1) → T
  27. Segment(Q, T) → f_1
  28. Point(d_1) → U
  29. Segment(U, S) → g_1
  30. Segment(V, W) → h_1
  31. Segment(V, C) → i_1
  32. Segment(W, S) → j_1
  33. Segment(D, W) → k_1
  34. Point(j) → Z
  35. Point(m) → A_1
  36. Segment(Z, A_1) → l_1
  37. Point(l_1) → B_1
  38. Segment(P, B_1) → m_1
  39. Point(l) → C_1
  40. Segment(B_1, C_1) → n_1
  41. Point(l_1) → D_1
  42. Segment(I, D_1) → p_1
  43. Point(n_1) → E_1
  44. Segment(J, E_1) → q_1
  45. Point(m_1) → F_1
  46. Segment(E, F_1) → r_1
  47. Point(l_1) → G_1
  48. Segment(B, G_1) → s_1
  49. Polygon(A, L, T, Q) → poly1, a_2, l_2, t_1, q_2
  50. Polygon(C_1, I, Z, B_1) → poly2, c_2, i_2, z, b_2
  51. Intersect(b, p) → H_1
  52. Polygon(C, M, H_1) → poly3, h_2, c_3, m_2
  53. Polygon(N, R, P, B) → poly4, n_2, r_2, p_2, b_3
  54. Intersect(a, b_1) → I_1
  55. Polygon(I_1, A, Q) → poly5, q_3, i_3, a_3
  56. Polygon(A_1, B_1, C_1, J) → poly6, a_4, b_4, c_4, j_2
  57. Polygon(D, W, U, O) → poly7, d_2, w, u, o
  58. Intersect(d, s) → J_1
  59. Polygon(B, N, J_1) → poly8, j_3, b_5, n_3
  60. Polygon(B_1, P, B, A_1) → poly9, b_6, p_3, b_7, a_5
  61. Polygon(M, C, V, S) → poly10, m_3, c_5, v, s_2
  62. Intersect(c, h_1) → K_1
  63. Polygon(W, K_1, D) → poly11, d_3, w_1, k_2
  64. Polygon(Z, E, P, B_1) → poly12, z_1, e_2, p_4, b_8
  65. Polygon(E, F, G, A) → poly13, e_3, f_2, g_2, a_6
  66. Polygon(R, T, S, U) → poly14, r_3, t_2, s_3, u_1
  67. Polygon(A, H_1, L) → poly15, l_3, a_7, h_3
  68. Polygon(H_1, M, C) → poly16, c_6, h_4, m_4
  69. Polygon(C, V, K_1) → poly17, k_3, c_7, v_1
  70. Polygon(K_1, D, W) → poly18, w_2, k_4, d_4
  71. Polygon(E, P, F_1) → poly19, f_3, e_4, p_5
  72. Polygon(I, D_1, Z) → poly20, z_2, i_4, d_5
  73. Polygon(C_1, E_1, J) → poly21, j_4, c_8, e_5
  74. Polygon(P, B, I_1) → poly22, i_5, p_6, b_9
  75. Polygon(I_1, Q, A) → poly23, a_8, i_6, q_4
  76. Polygon(G_1, A_1, B) → poly24, b_{10}, g_3, a_9
  77. Polygon(B, N, J_1) → poly25, j_5, b_{11}, n_4
  78. Polygon(D, O, J_1) → poly26, j_6, d_6, o_1
  79. Segment(F, E) → t_3
  80. Segment(E, A) → f_4
  81. Segment(A, G) → g_4
  82. Segment(G, F) → l_4
  83. Segment(E, B) → r_4
  84. Segment(B, A) → s_4
  85. Segment(A, C) → t_4
  86. Segment(C, D) → f_5
  87. Segment(D, B) → g_5
  88. Segment(B, J) → h_5
  89. Segment(J, I) → k_5
  90. Segment(I, E) → l_5
  91. Segment(Z, A_1) → m_5
  92. Segment(P, C_1) → n_5
  93. Segment(S, L) → q_5
  94. Segment(T, P) → r_5
  95. Segment(R, O) → s_5
  96. Segment(U, V) → t_5
  97. Segment(L, A) → e_6
  98. Segment(C, V) → f_6
  99. Segment(D, O) → g_6
  100. Intersect(k, l) → L_1
  101. Intersect(l_1, p_1) → M_1
  102. Segment(L_1, M_1) → h_6
  103. Segment(M_1, L_1) → k_6
  104. Intersect(n_1, q_1) → N_1
  105. Intersect(l, m) → O_1
  106. Segment(N_1, O_1) → l_6
  107. Segment(O_1, N_1) → m_6
  108. Segment(N_1, O_1) → n_6
  109. Segment(O_1, N_1) → q_6
  110. Segment(M_1, L_1) → r_6
  111. Segment(L_1, M_1) → s_6
  112. Segment(N_1, O_1) → t_6
  113. Point(l_1) → P_1
  114. Intersect(a, d) → Q_1
  115. Segment(P_1, Q_1) → d_7
  116. Segment(Q_1, P_1) → e_7
  117. Segment(P_1, Q_1) → f_7
  118. Segment(Q_1, P_1) → g_7
  119. Segment(P_1, Q_1) → h_7
  120. Segment(Q_1, P_1) → i_7
  121. Intersect(m_1, r_1) → R_1
  122. Intersect(e, f) → S_1
  123. Segment(R_1, S_1) → j_7
  124. Segment(S_1, R_1) → k_7
  125. Segment(R_1, S_1) → l_7
  126. Segment(S_1, R_1) → m_7
  127. Segment(R_1, S_1) → n_7
  128. Segment(S_1, R_1) → p_7
  129. Segment(R_1, S_1) → q_7
  130. Segment(Q_1, P_1) → r_7
  131. Segment(P_1, Q_1) → s_7
  132. Segment(R_1, S_1) → t_7
  133. Segment(S_1, R_1) → d_8
  134. Segment(R_1, S_1) → e_8
  135. Segment(S_1, R_1) → f_8
  136. Intersect(d, t) → T_1
  137. Intersect(s, t) → U_1
  138. Segment(T_1, U_1) → g_8
  139. Segment(U_1, T_1) → h_8
  140. Segment(T_1, U_1) → i_8
  141. Segment(U_1, T_1) → j_8
  142. Intersect(b_1, c_1) → V_1
  143. Intersect(a, b) → W_1
  144. Segment(V_1, W_1) → k_8
  145. Segment(W_1, V_1) → l_8
  146. Segment(V_1, W_1) → m_8
  147. Segment(W_1, V_1) → n_8
  148. Intersect(c, d) → Z_1
  149. Intersect(h_1, j_1) → A_2
  150. Segment(Z_1, A_2) → p_8
  151. Segment(A_2, Z_1) → q_8
  152. Segment(Z_1, A_2) → r_8
  153. Intersect(a, d) → B_2
  154. Point(l_1) → C_2
  155. Segment(B_2, C_2) → s_8
  156. Point(l_1) → D_2
  157. Intersect(f, n) → E_2
  158. Segment(D_2, E_2) → t_8
  159. Intersect(l, m) → F_2
  160. Intersect(n_1, q_1) → G_2
  161. Segment(F_2, G_2) → c_9
  162. Intersect(k, l) → H_2
  163. Intersect(l_1, p_1) → I_2
  164. Segment(H_2, I_2) → d_9
  165. Intersect(m_1, r_1) → J_2
  166. Intersect(e, f) → K_2
  167. Segment(J_2, K_2) → e_9