MathPlotAI Logo MathPlotAI

Map Coloring - Four Color Problem

Map Coloring - Four Color Problem
Loading the math board and drawing, please wait…
2020-06-16 13:30
FunctionGeometric ConstructionGraphing
This example demonstrates the application of the Four Color Theorem in map coloring, requiring the user to color regions so that no two adjacent regions share the same color. Key math concepts include graph theory, the Four Color Theorem, adjacency relations, and region partitioning. Construction involves commands like Segment for drawing boundaries, Polygon for forming regions, Sum for region summation, and CountIf for color usage statistics. Suitable for high school students, computer science enthusiasts, and those interested in graph theory.

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 map coloring example demonstrating the Four Color Theorem. Sketch multiple regions and boundary lines, ensuring adjacent regions have different colors. First, draw all the boundary lines, then fill in the regions, and finally color each region with different colors to illustrate the theorem. The map includes several interconnected regions that need careful coloring.
The prompt above was compiled from the original drawing commands and is for reference only.