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二项式乘法几何演示

二项式乘法几何演示
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2016-09-19 19:35
函数解析几何几何作图
所属专题 Algebra 1
这个范例演示了二项式的乘法过程。核心数学概念包括多项式乘法和几何表示。通过使用GeoGebra命令如Segment, RandomElement, Polynomial等，可以动态展示乘法过程中的每一项。适合初中及以上学生学习多项式的乘法和几何表示。

GeoGebra 命令及参数

  1. Segment(A, C) → f
  2. Segment(A, F) → g
  3. Segment(F, H) → h
  4. Segment(C, H) → i
  5. Segment(B, G) → j
  6. Segment(D, E) → k
  7. RandomElement(list1) → m
  8. RandomElement(list2) → n
  9. RandomElement(list3) → u
  10. RandomElement(list4) → v
  11. Polynomial((m * x) + u) → p
  12. Polynomial((n * x) + v) → q
  13. Polynomial((p(x) * q(x))) → r
  14. Polynomial(((m * x) * (n * x))) → s
  15. Polynomial(((n * x) * u)) → t
  16. Polynomial(((m * x) * v)) → f_1
  17. Polynomial((u * v)) → g_1
  18. Polynomial(((m + n) * x^(2))) → h_1
  19. Polynomial(((m + v) * x)) → p_1
  20. Polynomial(((n + u) * x)) → q_1
  21. Polynomial(u + v) → r_1
  22. Polynomial(((m * n) * x)) → s_1
  23. Intersect(g, h) → I
  24. Intersect(h, j) → J
  25. Intersect(j, k) → K
  26. Intersect(g, k) → L
  27. Distance(I, J) → distanceIJ
  28. Point(Circle[M, 2]) → N
  29. Segment(M, N) → l
  30. OrthogonalLine(M, l) → b
  31. OrthogonalLine(N, l) → c
  32. Distance(M, b) → distanceMb
  33. Point(Circle[M, 2]) → O
  34. Segment(M, O) → d
  35. Rotate(M, 270°, M) → M'
  36. Rotate(O, 270°, M) → O'
  37. Segment(M', O') → d'
  38. OrthogonalLine(O', d') → e
  39. Intersect(c, e) → P
  40. Polygon(M, N, P, O') → poly1, m_1, n_1, p_2, o'
  41. Distance(M, N) → distanceMN
  42. Point(Circle[Q, 2]) → R
  43. Segment(Q, R) → i_1
  44. Rotate(Q, 270°, Q) → Q'
  45. Rotate(R, 270°, Q) → R'
  46. Segment(Q', R') → j_1
  47. OrthogonalLine(R', j_1) → k_1
  48. OrthogonalLine(R, i_1) → l_1
  49. Intersect(k_1, l_1) → S
  50. Polygon(Q, R, S, R') → poly2, q_2, r_2, s_2, r'
  51. Distance(Q, R) → distanceQR
  52. Point(Circle[T, 2]) → U
  53. Segment(T, U) → t_1
  54. Rotate(T, 270°, T) → T'
  55. Rotate(U, 270°, T) → U'
  56. Segment(T', U') → c_8
  57. OrthogonalLine(U', c_8) → e_1
  58. OrthogonalLine(U, t_1) → f_2
  59. Intersect(e_1, f_2) → V
  60. Polygon(T, U, V, U') → poly3, t_2, u_1, v_1, u'
  61. Distance(T, U) → distanceTU
  62. Point(Circle[W, 2]) → Z
  63. Segment(W, Z) → g_2
  64. Rotate(W, 270°, W) → W'
  65. Rotate(Z, 270°, W) → Z'
  66. Segment(W', Z') → h_2
  67. OrthogonalLine(Z', h_2) → i_2
  68. OrthogonalLine(Z, g_2) → j_2
  69. Intersect(i_2, j_2) → A_1
  70. Polygon(W, Z, A_1, Z') → poly4, w, z_1, a_3, z'
  71. Distance(W, Z) → distanceWZ
  72. Point(Circle[B_1, 2]) → C_1
  73. Segment(B_1, C_1) → k_2
  74. Rotate(B_1, 270°, B_1) → D_1
  75. Rotate(C_1, 270°, B_1) → E_1
  76. Segment(D_1, E_1) → l_2
  77. OrthogonalLine(E_1, l_2) → m_2
  78. OrthogonalLine(C_1, k_2) → n_2
  79. Intersect(m_2, n_2) → F_1
  80. Polygon(B_1, C_1, F_1, E_1) → poly5, b_3, c_2, f_3, e_2
  81. Distance(B_1, C_1) → distanceB1C1
  82. Point(Circle[G_1, 2]) → H_1
  83. Segment(G_1, H_1) → g_3
  84. Rotate(G_1, 270°, G_1) → I_1
  85. Rotate(H_1, 270°, G_1) → J_1
  86. Segment(I_1, J_1) → h_3
  87. OrthogonalLine(J_1, h_3) → i_3
  88. OrthogonalLine(H_1, g_3) → j_3
  89. Intersect(i_3, j_3) → K_1
  90. Polygon(G_1, H_1, K_1, J_1) → poly6, g_4, h_4, k_3, j_4
  91. Distance(G_1, H_1) → distanceG1H1
  92. Point(Circle[L_1, 2]) → M_1
  93. Segment(L_1, M_1) → l_3
  94. Rotate(L_1, 270°, L_1) → N_1
  95. Rotate(M_1, 270°, L_1) → O_1
  96. Segment(N_1, O_1) → m_3
  97. OrthogonalLine(O_1, m_3) → n_3
  98. OrthogonalLine(M_1, l_3) → p_3
  99. Intersect(n_3, p_3) → P_1
  100. Polygon(L_1, M_1, P_1, O_1) → poly7, l_4, m_4, p_4, o_1
  101. Distance(L_1, M_1) → distanceL1M1
  102. Point(Circle[Q_1, 2]) → R_1
  103. Segment(Q_1, R_1) → q_3
  104. Rotate(Q_1, 270°, Q_1) → S_1
  105. Rotate(R_1, 270°, Q_1) → T_1
  106. Segment(S_1, T_1) → r_3
  107. OrthogonalLine(T_1, r_3) → s_3
  108. OrthogonalLine(R_1, q_3) → t_3
  109. Intersect(s_3, t_3) → U_1
  110. Polygon(Q_1, R_1, U_1, T_1) → poly8, q_4, r_4, u_2, t_4
  111. Distance(Q_1, R_1) → distanceQ1R1
  112. Point(Circle[V_1, 2]) → W_1
  113. Segment(V_1, W_1) → c_3
  114. Rotate(V_1, 270°, V_1) → Z_1
  115. Rotate(W_1, 270°, V_1) → A_2
  116. Segment(Z_1, A_2) → d_3
  117. OrthogonalLine(A_2, d_3) → e_3
  118. OrthogonalLine(W_1, c_3) → f_4
  119. Intersect(e_3, f_4) → B_2
  120. Polygon(V_1, W_1, B_2, A_2) → poly9, v_2, w_1, b_4, a_4
  121. Distance(V_1, W_1) → distanceV1W1
  122. Polynomial((p(x) * v)) → f_5
  123. Polynomial(((p(x) * n) * x)) → s_4
  124. Polynomial(s_4(x) + f_5(x)) → g_5
  125. Polynomial(((m * x) * q(x))) → h_5
  126. Polynomial((u * q(x))) → p_5
  127. Polynomial(h_5(x) + p_5(x)) → q_5