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Inequality Demonstration

Inequality Demonstration
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2020-02-08 01:02
Coordinate GeometryInequality
In collections Everything you want to know about inequalities without ever Everything you Want to Know about Inequalities (D Mentrard)
This example illustrates the representation and solution of inequalities in geometric figures. Key math concepts include inequalities, coordinate geometry, and geometric construction. It utilizes commands like Segment, Point, Sequence, If, Circle, OrthogonalLine, Intersect, Line in GeoGebra. Suitable for high school and above learners to understand the connection between inequalities and geometric shapes, as well as problem-solving techniques.

GeoGebra Commands & Parameters

  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