四色定理地图着色问题
几何画板及绘图内容加载中,请稍等……
①本范例演示了四色定理在地图着色中的应用,要求为地图的各个区域着色,使得相邻区域颜色不同;②涉及的核心数学概念为图论中的四色定理、相邻关系、区域划分;③作图要点:使用Segment命令绘制区域边界,Polygon命令形成封闭区域,Sum命令进行区域求和,CountIf命令统计颜色使用情况;④适合高中数学、计算机科学学生及对图论感兴趣的爱好者学习使用。
GeoGebra 命令及参数
Segment(A, C) → l_4Segment(C, Q_1) → k_5Segment(Q_1, O_1) → l_5Segment(O_1, A) → m_5Segment(B, E) → n_5Segment(D, H) → p_5Segment(D, P_1) → q_5Segment(I, J) → r_5Segment(J, U) → s_5Segment(O, R) → t_5Segment(P, K) → a_5Segment(K, L) → b_5Segment(L, F) → c_5Segment(Q, G) → d_5Segment(M, N) → f_6Segment(Z, A_1) → g_6Segment(A_1, H_1) → h_6Segment(H_1, J_1) → i_6Segment(I_1, V) → j_6Segment(U, W) → k_6Segment(W, C_1) → l_6Segment(B_1, D_1) → m_6Segment(F_1, B_1) → n_6Segment(E_1, G_1) → p_6Segment(G_1, M) → e_5Segment(X, Y) → q_6Segment(J_1, S) → r_6Segment(S, T) → s_6Segment(T, N_1) → t_6Segment(K_1, L_1) → a_6Segment(M_1, N_1) → b_6Polygon(B_1, D_1, G_1, F_1) → polígono1, b_7, d_6, g_7, f_7Polygon(V, W, C_1, B_1, F_1, E_1) → polígono2, v_3, w_3, c_6, b_8, f_8, e_6Polygon(O, R, D_1, C_1, W, U) → polígono3, o_3, r_7, d_7, c_7, w_4, u_3Polygon(X, Y, J_1, I_1, E_1, G_1) → polígono4, a_2, r_9, j_7, i_7, e_7, g_8Polygon(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_4Polygon(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}Polygon(F, G, Q, P, K, L) → polígono7, f_{10}, g_9, q_7, p_8, k_8, l_8Polygon(G, H, N, M, R, Q) → polígono8, g_{10}, h_8, n_7, m_7, r_8, q_8Polygon(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_9Polygon(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}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}Polygon(A, B, E, D, P_1, O_1) → polígono12, a_9, b_9, e_8, d_9, p_{10}, o_5Polygon(B, C, H, E) → polígono13, b_{10}, c_8, h_{10}, e_9Sum(frontera) → fmCountIf(ip ≟ 0, ip, pais) → pb
AI 绘图提示语参考
画一个地图着色示例,展示四色定理的应用。绘制多个区域和边界线,确保相邻区域颜色不同。先画出所有边界线,然后填充区域,最后用不同颜色标记每个区域,以展示四色定理。图形包含多个相连的区域,需要仔细着色。
以上提示语为根据原始绘图命令整理而来,仅供参考。