MathPlotAI Logo MathPlotAI

Traffic Matrix & Network Flow

Traffic Matrix & Network Flow
Loading the math board and drawing, please wait…
2019-07-29 09:08
VectorFunctionCoordinate GeometryMatrixInequality
This example demonstrates the relationship between traffic matrices and flow networks, showcasing the distribution of traffic flow through 2D vectors, linear equations, and matrix operations. Core mathematical concepts include 2D vectors, linear equations, matrix operations, intersection solving, and inequalities. Construction highlights are derived from GeoGebra commands: ReducedRowEchelonForm (Gaussian elimination), Simplify (simplification), Slope (slope calculation), RemoveUndefined (undefined removal), If (conditional logic), Intersect (intersection finding), Point (point creation), Polygon (polygon drawing), Textfield (text display), Sum (summation), LaTeX (formula rendering), Vector (vector operations); objects include xn2, yn2, yn1, xp2, yp1, xn1, xp1, yp2, m4, m5, f1, f2, f3, f4, mf1, mf2, mf3, bf1, bf2, bf3, bL, mL, fL, Lmin, Lmax, xmin, A, B, C, D, c1, a, b, c, d, E, F, G, H, c2. Suitable for high school and above, for understanding the application of linear algebra in traffic flow analysis.

GeoGebra Commands & Parameters

  1. ReducedRowEchelonForm(m4) → m5
  2. Simplify(Element[m5, 1, 5] - (x * Element[m5, 1, 4])) → f1
  3. Simplify(Element[m5, 2, 5] - (x * Element[m5, 2, 4])) → f2
  4. Simplify(Element[m5, 3, 5] - (x * Element[m5, 3, 4])) → f3
  5. Slope(f1) → mf1
  6. Slope(f2) → mf2
  7. Slope(f3) → mf3
  8. RemoveUndefined(Sequence[If[Element[mL, i] > 0 ∧ Element[bL, i] < 0, Element[Solutions[Element[fL, i]], 1]], i, 1, Length[bL]]) → Lmin
  9. RemoveUndefined(Sequence[If[Element[mL, i] < 0 ∧ Element[bL, i] > 0, Element[Solutions[Element[fL, i]], 1]], i, 1, Length[bL]]) → Lmax
  10. If(Length[Lmin] ≟ 0, 0, Max[Lmin]) → xmin
  11. Intersect(xAxis, yAxis) → A
  12. Point(yAxis) → B
  13. Point(xAxis) → D
  14. Polygon(A, B, C, D) → c1, a, b, c, d
  15. Point(yAxis) → E
  16. Point(yAxis) → H
  17. Polygon(E, F, G, H) → c2, e, f_1, g, h
  18. Point(yAxis) → I
  19. Point(yAxis) → L
  20. Polygon(I, J, K, L) → c3, i, j, k, l
  21. Polygon(M, N, O, P) → c4, m, n, o, p
  22. Polygon(Q, R, S, T) → c5, q, r, s, t
  23. Point(xAxis) → V
  24. Point(xAxis) → W
  25. Polygon(U, V, W, Z) → c6, u, v, w, z_1
  26. Point(xAxis) → A_1
  27. Point(xAxis) → B_1
  28. Polygon(A_1, B_1, C_1, D_1) → c7, a_1, b_1, c_1, d_1
  29. Polygon(E_1, F_1, G_1, H_1) → c8, e_1, g_1, h_1, i_1
  30. Polygon(I_1, J_1, K_1, L_1) → c9, j_1, k_1, l_1, m_1
  31. Polygon(A, B_1, L_1, L) → c10, a_2, n_5, p_1, l_2
  32. Textfield(yp1) → CasillaDeEntrada1
  33. Textfield(yp2) → CasillaDeEntrada2
  34. Textfield(xn1) → CasillaDeEntrada3
  35. Textfield(xn2) → CasillaDeEntrada4
  36. Textfield(yn1) → CasillaDeEntrada5
  37. Textfield(yn2) → CasillaDeEntrada6
  38. Textfield(xp1) → CasillaDeEntrada7
  39. Textfield(xp2) → CasillaDeEntrada8
  40. Sum(l3) → sumaSol
  41. LaTeX(sumaSol, true, true) → texto7
  42. Textfield(s_n) → CasillaDeEntrada9
  43. If(Length[Lmax] ≟ 0, If[xmin > 0, 1 / 0, 0], Min[Lmax]) → xmax
  44. Vector(T_1, S_1) → q_1
  45. Vector(V_1, U_1) → r_1
  46. Vector(A_2, B_2) → c_2
  47. Vector(C_2, D_2) → b_2
  48. Vector(E_2, F_2) → w_2
  49. Vector(N_1, M_1) → u_1
  50. Vector(P_1, O_1) → v_1
  51. Vector(R_1, Q_1) → w_1
  52. Vector(G_2, H_2) → t_1
  53. Vector(I_2, J_2) → u_2
  54. Vector(K_2, L_2) → v_2
  55. Vector(Z_1, W_1) → s_1