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Four Color Challenge

Four Color Challenge
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2018-05-26 05:32
Probability & StatisticsGeometric ConstructionGraphing
This example demonstrates the Four Color Theorem by allowing users to color a map using four colors (Blue, Green, Red, Purple) such that no two adjacent regions share the same color. It involves core math concepts in graph theory. Constructed using GeoGebra commands like Segment, Polygon, Sum, CountIf, and objects such as n, cB, cG, cR. Suitable for high school mathematics or computer science education on graph theory and algorithm design.

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 with 12 regions, each filled with one of four colors: blue, green, red, or purple, ensuring no two adjacent regions have the same color. Start by drawing the boundary lines, then fill in the colors.
The prompt above was compiled from the original drawing commands and is for reference only.