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Four Color Challenge by figen

Four Color Challenge by figen
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2018-01-17 03:10
Probability & StatisticsGeometric ConstructionGraphing
This example demonstrates the application of the Four Color Theorem in map coloring, requiring adjacent regions to have different colors. Key math concepts include graph theory, the Four Color Theorem, and adjacency relations between regions. GeoGebra commands used in construction are Segment, Polygon, Sum, and CountIf, along with objects like n (number of regions), color variables cB/cG/cR/cP (Blue/Green/Red/Purple), auxiliary objects aux, and text object texto2. It is suitable for middle school students and above to understand graph theory basics and logical reasoning, or as practice for math competitions or interest groups.

GeoGebra Commands & Parameters

  1. Segment(A, C) → l_4
  2. Segment(C, Q_1) → k_5
  3. Segment(Q_1, O_1) → l_5
  4. Segment(O_1, A) → m_5
  5. Segment(B, E) → n_5
  6. Segment(D, H) → p_5
  7. Segment(D, P_1) → q_5
  8. Segment(I, J) → r_5
  9. Segment(J, U) → s_5
  10. Segment(O, R) → t_5
  11. Segment(P, K) → a_5
  12. Segment(K, L) → b_5
  13. Segment(L, F) → c_5
  14. Segment(Q, G) → d_5
  15. Segment(M, N) → f_6
  16. Segment(Z, A_1) → g_6
  17. Segment(A_1, H_1) → h_6
  18. Segment(H_1, J_1) → i_6
  19. Segment(I_1, V) → j_6
  20. Segment(U, W) → k_6
  21. Segment(W, C_1) → l_6
  22. Segment(B_1, D_1) → m_6
  23. Segment(F_1, B_1) → n_6
  24. Segment(E_1, G_1) → p_6
  25. Segment(G_1, M) → e_5
  26. Segment(X, Y) → q_6
  27. Segment(J_1, S) → r_6
  28. Segment(S, T) → s_6
  29. Segment(T, N_1) → t_6
  30. Segment(K_1, L_1) → a_6
  31. Segment(M_1, N_1) → b_6
  32. Polygon(B_1, D_1, G_1, F_1) → polígono1, b_7, d_6, g_7, f_7
  33. Polygon(V, W, C_1, B_1, F_1, E_1) → polígono2, v_3, w_3, c_6, b_8, f_8, e_6
  34. Polygon(O, R, D_1, C_1, W, U) → polígono3, o_3, r_7, d_7, c_7, w_4, u_3
  35. Polygon(X, Y, J_1, I_1, E_1, G_1) → polígono4, a_2, r_9, j_7, i_7, e_7, g_8
  36. Polygon(I, J, U, V, I_1, H_1, A_1, Z) → polígono5, i_8, j_8, u_4, v_4, i_9, h_7, a_7, z_4
  37. Polygon(D, F, L, K, P, O, J, I) → polígono6, d_8, f_9, l_7, k_7, p_7, o_4, j_9, i_{10}
  38. Polygon(F, G, Q, P, K, L) → polígono7, f_{10}, g_9, q_7, p_8, k_8, l_8
  39. Polygon(G, H, N, M, R, Q) → polígono8, g_{10}, h_8, n_7, m_7, r_8, q_8
  40. Polygon(M, N, L_1, K_1, T, S, Y, X) → polígono9, m_8, n_8, l_9, k_9, t_7, s_7, s_9, t_9
  41. Polygon(S, T, N_1, M_1, Z, A_1, H_1, J_1) → polígono10, s_8, t_8, n_9, m_9, z_5, a_8, h_9, j_{10}
  42. Polygon(K_1, L_1, Q_1, P_1, M_1, N_1) → polígono11, k_{10}, l_{10}, q_9, p_9, m_{10}, n_{10}
  43. Polygon(A, B, E, D, P_1, O_1) → polígono12, a_9, b_9, e_8, d_9, p_{10}, o_5
  44. Polygon(B, C, H, E) → polígono13, b_{10}, c_8, h_{10}, e_9
  45. Sum(frontera) → fm
  46. CountIf(ip ≟ 0, ip, pais) → pb

AI Drawing Prompt Reference

Draw a planar map composed of multiple polygonal regions that are adjacent to each other, forming a complex jigsaw-like layout. The map contains about thirteen irregular polygons, each bounded by several line segments with vertices at various positions. All regions must be colored using four colors (blue, green, red, purple) such that any two regions sharing a boundary have different colors. To construct, first draw the boundary segments of each region, then connect vertices to form closed polygons, and finally count the number of regions and verify that adjacent regions satisfy the four-color theorem. The overall figure should clearly illustrate adjacency relations and coloring logic in graph theory.
The prompt above was compiled from the original drawing commands and is for reference only.