积极 AI Logo 积极 AI

不等式演示

不等式演示
几何画板及绘图内容加载中，请稍等……
2020-02-08 01:02
解析几何不等式
所属专题 Everything you want to know about inequalities without ever Everything you Want to Know about Inequalities (D Mentrard)
①本范例演示了不等式在几何图形中的表现与求解过程；②涉及的核心数学概念包括不等式、解析几何、几何作图；③作图要点：使用了Segment、Point、Sequence、If、Circle、OrthogonalLine、Intersect、Line等GeoGebra命令与对象；④适合高中及以上数学学习者，用于理解不等式与几何图形的关联及解题技巧。

GeoGebra 命令及参数

  1. Segment(U_1, V_1) → p_2
  2. Point(p_2) → W_1
  3. Segment(W_1, U_1) → t_2
  4. Segment(A, B) → a
  5. Point(a) → C
  6. Segment(D, E) → b
  7. Segment(F, G) → c
  8. Segment(H, I) → d
  9. Point(b) → J
  10. Point(c) → K
  11. Point(d) → L
  12. Segment(C, B) → e
  13. Sequence(C + (i, 0), i, 0, e, n) → liste1
  14. Segment(J, E) → f
  15. Sequence(J + (i, 0), i, 0, f, n) → liste2
  16. Segment(F, K) → g
  17. Sequence(K - (i, 0), i, 0, g, n) → liste3
  18. Segment(L, H) → h
  19. Sequence(L - (i, 0), i, 0, h, n) → liste4
  20. Sequence(C + (i, n), i, n, e, n) → liste5
  21. Sequence(C + (i, (-n)), i, 0, e, n) → liste6
  22. Sequence(Segment[Element[liste6, i], Element[liste5, i]], i, 0, e / n) → liste7
  23. Sequence(J + (i, n), i, n, f, n) → liste9
  24. Sequence(J + (i, (-n)), i, 0, f, n) → liste8
  25. Sequence(Segment[Element[liste8, i], Element[liste9, i]], i, 0, f / n) → liste10
  26. Sequence(K - (i, n), i, 0, g, n) → liste11
  27. Sequence(K - (i, (-n)), i, n, g, n) → liste12
  28. Sequence(Segment[Element[liste12, i], Element[liste11, i]], i, 0, g / n) → liste13
  29. Sequence(L - (i, (-n)), i, n, h, n) → liste14
  30. Sequence(L - (i, n), i, 0, h, n) → liste15
  31. Sequence(Segment[Element[liste14, i], Element[liste15, i]], i, 0, h / n) → liste16
  32. Segment(A, C) → i
  33. Segment(D, J) → j
  34. Segment(K, G) → k
  35. Segment(L, I) → l
  36. If(sign ≟ 1, "≤", If[sign ≟ 2, "<", If[sign ≟ 3, "≥", ">"]]) → signin
  37. If(sign ≟ 1, "]", If[sign ≟ 2, "[", If[sign ≟ 3, "[", "["]]) → croch2
  38. If(sign ≟ 1, "]", If[sign ≟ 2, "]", If[sign ≟ 3, "[", "]"]]) → croch1
  39. If(sign ≟ 1, "-∞", If[sign ≟ 2, " -∞", If[sign ≟ 3, "" + bb + " /" + aa, "" + bb + " /" + aa]]) → nomb1
  40. If(sign ≟ 1, " " + bb + " /" + aa, If[sign ≟ 2, " " + bb + "/" + aa, If[sign ≟ 3, "+∞", "+∞"]]) → nomb2
  41. Circle(C, (2 * n)) → p
  42. Circle(J, (2 * n)) → q
  43. Circle(K, (2 * n)) → r
  44. Circle(L, (2 * n)) → s
  45. OrthogonalLine(C, a) → t
  46. OrthogonalLine(J, b) → a_1
  47. OrthogonalLine(K, c) → b_1
  48. OrthogonalLine(L, d) → c_1
  49. Intersect(p, t) → M, N
  50. Intersect(q, a_1) → O, P
  51. Intersect(r, b_1) → Q, R
  52. Intersect(s, c_1) → S, T
  53. Segment(N, M) → d_1
  54. Segment(P, O) → e_1
  55. Segment(R, Q) → f_1
  56. Segment(T, S) → g_1
  57. Intersect(p, i) → U,
  58. Intersect(q, f) → V,
  59. Intersect(r, k) → W,
  60. Intersect(s, h) → Z,
  61. OrthogonalLine(U, a) → h_1
  62. OrthogonalLine(V, f) → i_1
  63. OrthogonalLine(W, k) → j_1
  64. OrthogonalLine(Z, h) → k_1
  65. Line(N, i) → l_1
  66. Line(M, i) → m_1
  67. Line(P, b) → n_1
  68. Line(O, b) → p_1
  69. Line(R, g) → q_1
  70. Line(Q, g) → r_1
  71. Line(T, l) → s_1
  72. Line(S, d) → t_1
  73. Intersect(l_1, h_1) → A_1
  74. Intersect(m_1, h_1) → B_1
  75. Intersect(n_1, i_1) → C_1
  76. Intersect(p_1, i_1) → D_1
  77. Intersect(j_1, q_1) → E_1
  78. Intersect(r_1, j_1) → F_1
  79. Intersect(s_1, k_1) → G_1
  80. Intersect(k_1, t_1) → H_1
  81. Segment(A_1, N) → a_2
  82. Segment(B_1, M) → b_2
  83. Segment(P, C_1) → c_2
  84. Segment(O, D_1) → d_2
  85. Segment(R, E_1) → e_2
  86. Segment(Q, F_1) → f_2
  87. Segment(T, G_1) → g_2
  88. Segment(S, H_1) → h_2
  89. Line(I_1, J_1) → i_2
  90. Line(K_1, L_1) → j_2
  91. Line(M_1, N_1) → k_2
  92. Point(i_2) → O_1
  93. Point(k_2) → P_1
  94. Line(O_1, P_1) → l_2
  95. Point(i_2) → Q_1
  96. Point(k_2) → R_1
  97. Line(Q_1, R_1) → m_2
  98. Point(i_2) → S_1
  99. Point(k_2) → T_1
  100. Line(S_1, T_1) → n_2
  101. Segment(U_1, W_1) → q_2
  102. Segment(W_1, V_1) → r_2
  103. If(sign ≟ 1, "]", If[sign ≟ 2, "[", If[sign ≟ 3, "[", "]"]]) → croch2droite
  104. Sequence(W_1 + (i, 0), i, 0, r_2, n) → liste17
  105. Sequence(W_1 + (i, n), i, n, r_2, n) → liste18
  106. Sequence(W_1 + (i, (-n)), i, 0, r_2, n) → liste19
  107. Sequence(Segment[Element[liste19, i], Element[liste18, i]], i, 0, r_2 / n) → liste20
  108. Sequence(W_1 - (i, n), i, 0, t_2, n) → liste22
  109. Sequence(W_1 - (i, 0), i, 0, q_2, n) → liste21
  110. Sequence(W_1 - (i, (-n)), i, n, t_2, n) → liste23
  111. Segment(W_1, V_1) → s_2
  112. Sequence(Segment[Element[liste22, i], Element[liste23, i]], i, 0, t_2 / n) → liste24
  113. Segment(O_1, P_1) → a_3
  114. Segment(Q_1, R_1) → b_3
  115. Segment(J_1, N_1) → c_3
  116. Segment(I_1, M_1) → d_3
  117. Intersect(j_2, d_3) → Z_1
  118. Intersect(c_3, j_2) → A_2
  119. Segment(I_1, J_1) → e_3
  120. Segment(Z_1, A_2) → f_3
  121. Segment(M_1, N_1) → g_3
  122. Segment(S_1, T_1) → h_3
  123. Circle(W_1, (2 * n)) → k_3
  124. OrthogonalLine(W_1, p_2) → i_3
  125. Intersect(k_3, i_3) → B_2, C_2
  126. Intersect(p_2, r_2) → D_2
  127. Intersect(k_3, r_2) → E_2,
  128. OrthogonalLine(E_2, r_2) → j_3
  129. Line(C_2, r_2) → l_3
  130. Line(B_2, p_2) → m_3
  131. Intersect(l_3, j_3) → F_2
  132. Intersect(j_3, m_3) → G_2
  133. Segment(F_2, C_2) → n_3
  134. Segment(G_2, B_2) → p_3
  135. Intersect(k_3, q_2) → H_2,
  136. OrthogonalLine(H_2, q_2) → q_3
  137. Intersect(l_3, q_3) → I_2
  138. Intersect(m_3, q_3) → J_2
  139. Segment(C_2, I_2) → r_3
  140. Segment(B_2, J_2) → s_3
  141. Segment(C_2, B_2) → t_3
  142. Segment(K_2, L_2) → a_4
  143. Segment(L_2, M_2) → b_4
  144. Segment(N_2, M_2) → c_4
  145. Segment(N_2, K_2) → d_4