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勾股定理演示 by GaëlleJ

勾股定理演示 by GaëlleJ
几何画板及绘图内容加载中，请稍等……
2013-03-12 04:04
测试改名0圆向量几何作图
①本范例演示直角三角形三边长度关系，即勾股定理；②涉及核心数学概念为勾股定理、直角三角形、向量与几何变换；③构造过程中使用 GeoGebra 命令/对象包括：Segment（线段）、OrthogonalLine（垂线）、Point（点）、Polygon（多边形）、AngularBisector（角平分线）、Intersect（交点）、Vector（向量）、Translate（平移）、Circle（圆）；④适合初中及以上学生学习几何作图与定理验证，也可用于数学教学演示。

GeoGebra 命令及参数

  1. Segment(A, B) → a
  2. OrthogonalLine(B, a) → b
  3. Point(b) → C
  4. Segment(B, C) → c
  5. Polygon(A, C, B) → veelhoek1, b_1, a_1, c_1
  6. Polygon(A, C, 4) → veelhoek2, a_2, c_2, d, e, D, E
  7. Polygon(C, B, 4) → veelhoek3, c_3, b_2, f, g, F, G
  8. Polygon(B, A, 4) → veelhoek4, b_3, a_3, h, i, H, I
  9. AngularBisector(a, c) → j, k
  10. Intersect(k, b_1) → J
  11. OrthogonalLine(J, c) → l
  12. OrthogonalLine(J, a) → m
  13. Intersect(m, a) → K
  14. Intersect(b, l) → L
  15. Polygon(K, J, L, B) → veelhoek5, k_1, j_1, l_1, b_4
  16. OrthogonalLine(A, a) → n
  17. Intersect(l, n) → M
  18. Polygon(A, M, J) → veelhoek6, j_2, a_4, m_1
  19. Intersect(l, e) → N
  20. Polygon(N, M, A) → veelhoek7, a_5, n_1, m_2
  21. OrthogonalLine(D, a_4) → p
  22. Intersect(l, p) → S
  23. OrthogonalLine(N, c_2) → q
  24. OrthogonalLine(J, q) → r
  25. Intersect(p, q) → O
  26. Intersect(q, c_2) → P
  27. Polygon(J, O, P, C) → veelhoek8, j_3, o, p_1, c_4
  28. Vector(O, L) → u
  29. Translate(J, u) → J'
  30. Translate(O, u) → O'
  31. Translate(P, u) → P'
  32. Translate(C, u) → C'
  33. Polygon(J', O', P', C') → veelhoek8', j', o', p', c'
  34. Intersect(r, d) → Q
  35. Polygon(N, E, Q, O) → veelhoek9, n_2, e_1, q_1, o_1
  36. Vector(Q, K) → v
  37. Translate(N, v) → N'
  38. Translate(E, v) → E'
  39. Translate(Q, v) → Q'
  40. Translate(O, v) → O'_1
  41. Polygon(N', E', Q', O'_1) → veelhoek9', n', e', q', o'_1
  42. OrthogonalLine(Q, p) → s
  43. OrthogonalLine(P, p) → t
  44. Intersect(p, s) → R
  45. Intersect(p, t) → T
  46. Polygon(Q, R, D) → veelhoek10, d_1, q_2, r_1
  47. Polygon(P, T, O) → veelhoek11, o_2, p_2, t_1
  48. Polygon(P, T, D) → veelhoek12, d_2, p_3, t_2
  49. Polygon(R, Q, O) → veelhoek13, o_3, r_2, q_3
  50. Polygon(S, N, O) → veelhoek14, o_4, s_1, n_3
  51. Polygon(J, S, O) → veelhoek15, o_5, j_4, s_2
  52. Polygon(K, A, E') → veelhoek16, e'_1, k_2, a_6
  53. Polygon(B, K, O'_1) → veelhoek17, o'_2, b_5, k_3
  54. Polygon(E', H, N') → veelhoek18, n'_1, e'_2, h_1
  55. Polygon(N', I, O'_1) → veelhoek19, o'_3, n'_2, i_1
  56. Polygon(J', B, L) → veelhoek20, l_2, j'_1, b_6
  57. Polygon(L, C, P') → veelhoek21, p'_1, l_3, c_5
  58. Polygon(P', G, C') → veelhoek22, c'_1, p'_2, g_1
  59. Polygon(C', J', F) → veelhoek23, f_1, c'_2, j'_2
  60. Segment(E', E) → e_2
  61. Circle(E', verschuiving * Distance[E', E]) → f_2
  62. Intersect(f_2, e_2, 1) → U
  63. Vector(E', U) → w
  64. Translate(N', w) → N''
  65. Translate(E', w) → E''
  66. Translate(Q', w) → Q''
  67. Translate(O'_1, w) → V
  68. Polygon(N'', E'', Q'', V) → veelhoek9'', n'', e'', q'', v_1
  69. Segment(P', P) → g_2
  70. Circle(P', verschuiving * Distance[P', P]) → h_2
  71. Intersect(h_2, g_2, 1) → W
  72. Vector(P', W) → z
  73. Translate(L, z) → L'
  74. Translate(C, z) → C'_1
  75. Translate(P', z) → P''
  76. Polygon(L', C'_1, P'') → veelhoek21', p'', l', c'_3
  77. Segment(C', D) → i_2
  78. Circle(C', verschuiving * Distance[C', D]) → d_3
  79. Intersect(d_3, i_2, 1) → Z
  80. Vector(C', Z) → u_1
  81. Translate(C', u_1) → C''
  82. Translate(J', u_1) → J''
  83. Translate(F, u_1) → F'
  84. Polygon(C'', J'', F') → veelhoek23', f', c'', j''
  85. Segment(J', J) → e_3
  86. Circle(J', verschuiving * Distance[J', J]) → f_3
  87. Intersect(f_3, e_3, 1) → A_1
  88. Vector(J', A_1) → w_1
  89. Translate(J', w_1) → J''_1
  90. Translate(B, w_1) → B'
  91. Translate(L, w_1) → L'_1
  92. Polygon(J''_1, B', L'_1) → veelhoek20', l'_1, j''_1, b'
  93. Segment(P', N) → g_3
  94. Circle(P', verschuiving * Distance[P', N]) → h_3
  95. Intersect(h_3, g_3, 1) → B_1
  96. Vector(P', B_1) → z_1
  97. Translate(P', z_1) → P''_1
  98. Translate(G, z_1) → G'
  99. Translate(C', z_1) → C''_1
  100. Polygon(P''_1, G', C''_1) → veelhoek22', c''_1, p''_1, g'
  101. Translate(J', z) → J''_2
  102. Translate(O', z) → O''
  103. Translate(P', z) → P''_2
  104. Translate(C', z) → C''_2
  105. Polygon(J''_2, O'', P''_2, C''_2) → veelhoek8'', j''_2, o'', p''_2, c''_2
  106. Segment(K, Q) → i_3
  107. Circle(K, verschuiving * Distance[Q', Q]) → r_3
  108. Intersect(q'', e'') → C_1
  109. Vector(K, Q'') → u_2
  110. Translate(B, u_2) → B'_1
  111. Translate(K, u_2) → K'
  112. Translate(O'_1, u_2) → D_1
  113. Polygon(B'_1, K', D_1) → veelhoek17', d_4, b'_1, k'
  114. Segment(H, T) → m_3
  115. Circle(H, verschuiving * Distance[H, T]) → s_3
  116. Intersect(a_2, m_1) → E_1
  117. Intersect(a_2, m_1) → F_1
  118. Intersect(a_2, m_1) → G_1
  119. Intersect(s_3, m_3, 1) → H_1
  120. Vector(H, H_1) → v_2
  121. Translate(E', v_2) → E''_1
  122. Translate(H, v_2) → H'
  123. Translate(N', v_2) → N''_1
  124. Polygon(E''_1, H', N''_1) → veelhoek18', n''_1, e''_1, h'
  125. Segment(I, S) → t_3
  126. Circle(I, verschuiving * Distance[I, S]) → e_4
  127. Intersect(e_4, t_3, 1) → I_1
  128. Vector(I, I_1) → w_2
  129. Translate(N', w_2) → N''_2
  130. Translate(I, w_2) → I'
  131. Translate(O'_1, w_2) → J_1
  132. Polygon(N''_2, I', J_1) → veelhoek19', j_5, n''_2, i'
  133. Segment(A, M) → f_4
  134. Segment(E', A) → g_4
  135. Circle(E', verschuiving * Distance[E', A]) → h_4
  136. Intersect(a_3, k_2) → K_1
  137. Intersect(a_3, k_2) → L_1
  138. Intersect(a_3, k_2) → M_1
  139. Intersect(a_3, k_2) → N_1
  140. Intersect(a_3, k_2) → O_1
  141. Intersect(h_4, a_3, 1) → P_1
  142. Vector(E', P_1) → z_2
  143. Translate(K, z_2) → K'_1
  144. Translate(A, z_2) → A'
  145. Translate(E', z_2) → E''_2
  146. Polygon(K'_1, A', E''_2) → veelhoek16', e''_2, k'_1, a'

AI 绘图提示语参考

画一个直角三角形，标注出两条直角边的长度，并展示通过构造和旋转这些边形成的图形，最终验证勾股定理。首先画出直角三角形，然后从直角顶点向一条直角边作垂线，并利用垂线和向量构造新的图形，通过平移和旋转这些图形，最终形成多个相互关联的多边形，直观展示勾股定理的几何意义。
以上提示语为根据原始绘图命令整理而来，仅供参考。