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(a - b)² 几何演示

(a - b)² 几何演示
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2020-01-18 16:25
向量解析几何几何作图
所属专题 Algebraic puzzles for binomial formula
①本范例通过动态演示 (a - b)² 的代数表达式在几何空间中的表现；②涉及核心数学概念包括代数表达式、向量、距离、旋转和平移；③构造过程中使用了 Line, Point, Polygon, Intersect, Midpoint, Vector, RotateText, Translate, Distance, Segment 等GeoGebra命令和对象；④适合高中数学教学，用于理解代数与几何的联系，提升空间想象能力。

GeoGebra 命令及参数

  1. Line(A, xAxis) → a
  2. Point(a) → B
  3. Polygon(B, A, 4) → poly1, b_1, c, d, e, C, D
  4. Line(A, C) → f
  5. Point(c) → E
  6. Polygon(A, E, 4) → poly2, g, h, i, j, F, G
  7. Line(G, F) → k
  8. Line(E, F) → l
  9. Line(H, a) → m
  10. Line(I, f) → n
  11. Line(L, k) → p
  12. Line(K, d) → q
  13. Line(C, D) → r
  14. Line(B, D) → s
  15. Intersect(r, d) → M
  16. Intersect(k, r) → N
  17. Intersect(k, m) → O
  18. Intersect(m, s) → P
  19. Intersect(r, n) → Q
  20. Intersect(q, k) → R
  21. Midpoint(O, P) → S
  22. Midpoint(H, O) → T
  23. Intersect(l, p) → U
  24. Line(W, a) → t
  25. Line(V, n) → a_1
  26. Intersect(a_1, r) → Z
  27. Intersect(s, t) → A_1
  28. Midpoint(W, A_1) → B_1
  29. Vector(B_1, A_1) → u
  30. Vector(B_1, W) → v
  31. Midpoint(V, Z) → C_1
  32. Vector(C_1, V) → w
  33. Vector(C_1, Z) → z
  34. Vector(T, O) → b
  35. Vector(T, H) → u_1
  36. Midpoint(J, Q) → D_1
  37. Midpoint(I, J) → E_1
  38. Midpoint(K, R) → F_1
  39. Intersect(s, q) → G_1
  40. Vector(S, P) → v_1
  41. Vector(S, O) → w_1
  42. Vector(D_1, J) → z_1
  43. Vector(D_1, Q) → c_1
  44. Vector(F_1, R) → d_1
  45. Vector(F_1, K) → e_1
  46. Midpoint(R, G_1) → H_1
  47. RotateText(texte5, 90°) → texte7
  48. Vector(H_1, G_1) → f_1
  49. Vector(H_1, R) → g_1
  50. Vector(E_1, I) → h_1
  51. Vector(E_1, J) → i_1
  52. Midpoint(G, E) → I_1
  53. Intersect(s, e) → N_1
  54. Intersect(l, s) → O_1
  55. Polygon(G, B, O_1, F) → poly3, n_1, p_1, b_2, d_2
  56. Vector(F, K_1) → j_1
  57. Polygon(E, F, N, C) → poly4, t_1, c_2, e_2, h_2
  58. Vector(C, L_1) → k_1
  59. Polygon(F, O_1, D, N) → poly5, f_2, o_2, d_4, n_2
  60. Vector(N, M_1) → l_1
  61. Translate(G, Vector[(Animation / 10 * j_1)]) → G'
  62. Translate(B, Vector[(Animation / 10 * j_1)]) → B'
  63. Translate(D, Vector[(Animation / 10 * j_1)]) → D'
  64. Vector(C, J_1) → m_1
  65. Translate(E, Vector[(Animation / 10 * k_1)]) → E'
  66. Translate(O_1, Vector[(Animation / 10 * k_1)]) → P_1
  67. Translate(D, Vector[(Animation / 10 * k_1)]) → D'_1
  68. Translate(F, Vector[(Animation / 10 * l_1)]) → F'
  69. Translate(O_1, Vector[(Animation / 10 * l_1)]) → Q_1
  70. Translate(D, Vector[(Animation / 10 * l_1)]) → D'_2
  71. Translate(N, Vector[(Animation / 10 * l_1)]) → N'_1
  72. Polygon(F', Q_1, D'_2, N'_1) → poly5', f', q_1, d'_2, n'_1
  73. Polygon(A, G, F, E) → poly6, a_2, g_3, f_3, e_3
  74. Translate(A, Vector[(Animation / 10 * m_1)]) → A'
  75. Translate(G, Vector[(Animation / 10 * m_1)]) → G'_1
  76. Translate(F, Vector[(Animation / 10 * m_1)]) → F'_1
  77. Translate(E, Vector[(Animation / 10 * m_1)]) → E'_1
  78. Polygon(A', G'_1, F'_1, E'_1) → poly6', a', g'_1, f'_1, e'_1
  79. Polygon(A, B, D, C) → poly7, a_3, b_3, d_5, c_3
  80. Translate(A, Vector[(Animation / 10 * m_1)]) → A'_1
  81. Translate(B, Vector[(Animation / 10 * m_1)]) → B'_1
  82. Translate(D, Vector[(Animation / 10 * m_1)]) → D'_3
  83. Translate(C, Vector[(Animation / 10 * m_1)]) → C'_1
  84. Polygon(A'_1, B'_1, D'_3, C'_1) → poly7', a'_1, b'_1, d'_3, c'_1
  85. Line(E'_1, F'_1) → r_1
  86. Line(G'_1, F'_1) → s_1
  87. Intersect(r_1, b'_1) → T_1
  88. Intersect(s_1, d'_3) → U_1
  89. Translate(E, Vector[(Animation / 10 * k_1)]) → E'_2
  90. Translate(F, Vector[(Animation / 10 * k_1)]) → F'_2
  91. Translate(N, Vector[(Animation / 10 * k_1)]) → N'_2
  92. Translate(C, Vector[(Animation / 10 * k_1)]) → C'
  93. Polygon(E'_2, F'_2, N'_2, C') → poly4', e'_2, f'_2, n'_2, c'
  94. Translate(G, Vector[(Animation / 10 * j_1)]) → G'_2
  95. Translate(B, Vector[(Animation / 10 * j_1)]) → B'_2
  96. Translate(O_1, Vector[(Animation / 10 * j_1)]) → R_1
  97. Translate(F, Vector[(Animation / 10 * j_1)]) → F'_3
  98. Polygon(G'_2, B'_2, R_1, F'_3) → poly3', g'_2, b'_2, r_2, f'_3
  99. Midpoint(B', F'_3) → S_1
  100. Midpoint(E', N'_2) → V_1
  101. Midpoint(A', F'_1) → W_1
  102. Midpoint(F, A) → Z_1
  103. Midpoint(F', D'_2) → A_2
  104. Distance(F'_1, K_1) → aa
  105. Distance(C'_1, L_1) → bb
  106. Midpoint(A', D'_3) → B_2
  107. Line(G'_1, F'_1) → g_2
  108. Intersect(g_2, d'_3) → C_2
  109. Distance(M_1, C_2) → cc
  110. Intersect(d'_3, b'_1) → D_2
  111. Segment(E_2, F_2) → i_2
  112. Segment(G_2, H_2) → j_2

AI 绘图提示语参考

绘制一个动态几何演示图，展示代数式(a-b)²的几何意义。先画一条水平直线，在其上取一点作为正方形的一个顶点，构造一个大正方形。在大正方形内部，从一条边上取一点，构造一个小正方形，使其顶点与大正方形顶点相连。接着，通过连接各顶点和交点，画出多条辅助线段，形成网格状结构。标记出各线段的中点，并从中点向相邻顶点绘制向量箭头，表示平移和距离关系。最后，将一段文字旋转90度，放置在图形中，以标注相关表达式或说明。整体图形由正方形、线段、交点和向量构成，体现代数与几何的对应关系。
以上提示语为根据原始绘图命令整理而来，仅供参考。