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MMC Example 2

MMC Example 2
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2020-11-06 09:12
OptimizationGeometric Construction
This example demonstrates the geometric construction of the MMC (Maximum Minimum Condition) problem. Key mathematical concepts include geometric construction, optimization, and linear programming. Using GeoGebra commands such as Point, Polygon, Midpoint, etc., users can intuitively understand how to find the optimal solution through geometric construction.

GeoGebra Commands & Parameters

  1. Point(xAxis) → U
  2. Point(xAxis) → V
  3. Polygon(U, V, 4) → pol6, n, p, b, h_1, W, Z
  4. Midpoint(n) → A_1
  5. OrthogonalLine(A_1, n) → i_1
  6. Midpoint(p) → B_1
  7. OrthogonalLine(B_1, i_1) → m_1
  8. Intersect(i_1, m_1) → C_1
  9. Circle(C_1, (sqrt(31) - 1) / 5) → c_1
  10. Intersect(c_1, m_1, 2) → D_1
  11. Intersect(c_1, i_1) → E_1, F_1
  12. Mirror(D_1, i_1) → G_1
  13. Line(D_1, i_1) → n_1
  14. Line(E_1, m_1) → p_1
  15. Intersect(n_1, p_1) → H_1
  16. Mirror(H_1, i_1) → I_1
  17. Mirror(I_1, m_1) → J_1
  18. Mirror(J_1, i_1) → K_1
  19. Midpoint(K_1, F_1) → L_1
  20. Line(K_1, J_1) → d_1
  21. Circle(L_1, 0.15) → e_1
  22. Intersect(e_1, d_1) → M_1, N_1
  23. OrthogonalLine(L_1, d_1) → f_2
  24. Circle(L_1, (4 - (4 * (sqrt(31) - 1) / 5)) / 3) → c_2
  25. Intersect(f_2, pol6) → O_1, P_1
  26. Intersect(c_2, f_2) → Q_1, R_1
  27. OrthogonalLine(Q_1, f_2) → i_2
  28. OrthogonalLine(M_1, d_1) → k_2
  29. OrthogonalLine(N_1, d_1) → n_2
  30. Intersect(i_2, k_2) → S_1
  31. Intersect(i_2, n_2) → V_1
  32. Intersect(h_1, m_1) → W_1
  33. Intersect(i_1, b) → Z_1
  34. Polygon(Z, W_1, D_1, K_1, M_1, S_1, V_1, N_1, F_1, Z_1) → pol4, z_1, i_3, w_1, t_2, a_2, b_2, d_2, v_1, e_2, h_3
  35. Mirror(Z, i_1) → Z'
  36. Mirror(W_1, i_1) → A
  37. Mirror(D_1, i_1) → B
  38. Mirror(K_1, i_1) → C
  39. Mirror(M_1, i_1) → D
  40. Mirror(S_1, i_1) → E
  41. Mirror(V_1, i_1) → F
  42. Mirror(N_1, i_1) → G
  43. Mirror(F_1, i_1) → H
  44. Mirror(Z_1, i_1) → I
  45. Polygon(Z', A, B, C, D, E, F, G, H, I) → pol5, z', i, a, b_1, c, d, e, f, g, h
  46. Mirror(Z, m_1) → Z'_{1}
  47. Mirror(W_1, m_1) → J
  48. Mirror(D_1, m_1) → K
  49. Mirror(K_1, m_1) → L
  50. Mirror(M_1, m_1) → M
  51. Mirror(S_1, m_1) → N
  52. Mirror(V_1, m_1) → O
  53. Mirror(N_1, m_1) → P
  54. Mirror(F_1, m_1) → Q
  55. Mirror(Z_1, m_1) → R
  56. Polygon(Z'_{1}, J, K, L, M, N, O, P, Q, R) → pol3, z'_{1}, r, j, k, l, m, n_3, o, p_2, q
  57. Mirror(Z', m_1) → Z''
  58. Mirror(A, m_1) → A'
  59. Mirror(B, m_1) → B'
  60. Mirror(C, m_1) → C'
  61. Mirror(D, m_1) → D'
  62. Mirror(E, m_1) → E'
  63. Mirror(F, m_1) → F'
  64. Mirror(G, m_1) → G'
  65. Mirror(H, m_1) → H'
  66. Mirror(I, m_1) → I'
  67. Polygon(Z'', A', B', C', D', E', F', G', H', I') → pol2, z'', i', a', b', c', d', e', f', g', h'
  68. Polygon(K_1, H_1, I_1, J_1, D, E, F, G, N_1, V_1, S_1, M_1, M, N, O, P, G', F', E', D') → pol1, k_1, j_1, l_1, q_1, d_3, e_3, f_3, g_2, r_1, s_1, t_1, s, a_1, m_2, n_4, o_1, p_3, t, f_1, g_1
  69. Perimeter(pol2) → Perímetro_{pol2}
  70. Perimeter(pol1) → Perímetro_{pol1}
  71. Prism(pol3, n) → h_2, S, F_2, face1, face2, face3, face4, face5, face6, face7, face8, face9, T, face10, face11, aresta1, aresta2, aresta3, aresta4, aresta5, aresta6, aresta7, aresta8, T_1, aresta9, aresta10, aresta11, aresta12, aresta13, aresta14, aresta15, aresta16, aresta17, aresta18, U_1, aresta19, aresta20, A_2, B_2, C_2, D_2, E_2

AI Drawing Prompt Reference

Place two points on the x-axis and use them to form a square. Find the midpoint of one side and draw a perpendicular line through it; then take the midpoint of an adjacent side and draw a line perpendicular to that perpendicular, intersecting at a center point. Using this center, draw a circle with a specific radius, intersecting the perpendicular lines at several points. Through reflections and connections, construct a polygon from these points, then mirror it across a line to create a symmetric counterpart. The final figure shows a symmetric arrangement of circles, perpendicular lines, and polygons.
The prompt above was compiled from the original drawing commands and is for reference only.