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Parabolic Triangle

Parabolic Triangle
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2018-06-17 23:24
TriangleFunctionCalculusInequalityGeometric Construction
This example demonstrates the construction and properties of a parabolic triangle, involving core math concepts like real numbers, median value, upper and lower sum/Riemann sum, inequalities, and 2D vectors. It is constructed using GeoGebra commands such as Segment and Midpoint, suitable for high school and above, particularly in calculus education.

GeoGebra Commands & Parameters

  1. Segment(A, B) → f
  2. Segment(B, C) → g
  3. Segment(C, A) → h
  4. Midpoint(f) → D
  5. Midpoint(B, D) → E
  6. Midpoint(B, E) → F
  7. Midpoint(B, F) → G
  8. Midpoint(F, E) → H
  9. Midpoint(E, D) → I
  10. Midpoint(D, I) → J
  11. Midpoint(I, E) → K
  12. Midpoint(D, A) → L
  13. Midpoint(L, A) → M
  14. Midpoint(L, M) → N
  15. Midpoint(M, A) → O
  16. Midpoint(L, D) → P
  17. Midpoint(D, P) → Q
  18. Midpoint(D, L) → R
  19. Midpoint(P, D) → S
  20. Midpoint(L, P) → T
  21. Midpoint(B, C) → U
  22. Midpoint(U, B) → V
  23. Midpoint(U, V) → W
  24. Midpoint(V, B) → Z
  25. Midpoint(B, Z) → A_1
  26. Midpoint(Z, V) → B_1
  27. Midpoint(V, W) → C_1
  28. Midpoint(W, U) → D_1
  29. Midpoint(U, C) → E_1
  30. Midpoint(E_1, U) → F_1
  31. Midpoint(U, F_1) → G_1
  32. Midpoint(F_1, E_1) → H_1
  33. Midpoint(E_1, C) → I_1
  34. Midpoint(C, I_1) → J_1
  35. Midpoint(I_1, E_1) → K_1
  36. Midpoint(C, A) → L_1
  37. Midpoint(A, L_1) → M_1
  38. Midpoint(L_1, M_1) → N_1
  39. Midpoint(M_1, A) → O_1
  40. Midpoint(A, O_1) → P_1
  41. Midpoint(O_1, M_1) → Q_1
  42. Midpoint(M_1, N_1) → R_1
  43. Midpoint(N_1, L_1) → S_1
  44. Midpoint(L_1, C) → T_1
  45. Midpoint(C, T_1) → U_1
  46. Midpoint(C, U_1) → V_1
  47. Midpoint(U_1, T_1) → W_1
  48. Midpoint(T_1, L_1) → Z_1
  49. Midpoint(L_1, Z_1) → A_2
  50. Midpoint(Z_1, T_1) → B_2
  51. Segment(G, J_1) → i
  52. Segment(F, I_1) → j
  53. Segment(H, K_1) → k
  54. Segment(E, E_1) → l
  55. Segment(K, H_1) → m
  56. Segment(I, F_1) → n
  57. Segment(J, G_1) → p
  58. Segment(D, U) → q
  59. Segment(Q, D_1) → r
  60. Segment(P, W) → s
  61. Segment(T, C_1) → t
  62. Segment(L, V) → a
  63. Segment(N, B_1) → b
  64. Segment(M, Z) → c
  65. Segment(O, A_1) → d
  66. Segment(V_1, A_1) → e
  67. Segment(U_1, Z) → f_1
  68. Segment(B_1, W_1) → g_1
  69. Segment(T_1, V) → h_1
  70. Segment(B_2, C_1) → i_1
  71. Segment(Z_1, W) → j_1
  72. Segment(A_2, D_1) → k_1
  73. Segment(L_1, U) → l_1
  74. Segment(S_1, G_1) → m_1
  75. Segment(N_1, F_1) → n_1
  76. Segment(R_1, H_1) → p_1
  77. Segment(M_1, E_1) → q_1
  78. Segment(Q_1, K_1) → r_1
  79. Segment(O_1, I_1) → s_1
  80. Segment(P_1, J_1) → t_1
  81. Segment(O, V_1) → a_1
  82. Segment(M, U_1) → b_1
  83. Segment(N, W_1) → c_1
  84. Segment(L, T_1) → d_1
  85. Segment(T, B_2) → e_1
  86. Segment(P, Z_1) → f_2
  87. Segment(Q, A_2) → g_2
  88. Segment(D, L_1) → h_2
  89. Segment(D, J) → i_2
  90. Segment(J, S_1) → j_2
  91. Segment(I, N_1) → k_2
  92. Segment(K, R_1) → l_2
  93. Segment(E, M_1) → m_2
  94. Segment(H, Q_1) → n_2
  95. Segment(F, H) → p_2
  96. Segment(F, O_1) → q_2
  97. Segment(G, P_1) → r_2
  98. Segment(C, B) → s_2