四色定理的GeoGebra可视化演示

几何画板及绘图内容加载中，请稍等……

2018-07-03 03:58

所属专题 The Best Math Book in the World

该范例通过GeoGebra交互式图形展示四色定理（Four Color Theorem）的核心思想：任何平面地图都可以用不超过四种颜色对区域进行着色，使得相邻区域颜色不同。涉及的核心数学概念包括图论中的平面图着色、区域邻接关系以及组合优化中的最小着色数问题。作图要点方面，构造摘要显示使用了Polygon（多边形）构建地图区域，Point（点）和Line（线）定义边界，Mirror（镜像）和Intersect（交点）生成对称或复杂邻接结构，Sum（求和）、Min（最小值）、KeepIf（筛选）和Length（长度）用于处理颜色分配与验证条件，对象列表包含大量顶点（A至S）和边（a至i_1）以及辅助点（p01、p02等），整体通过GeoGebra命令实现区域划分与着色逻辑。该范例适合高中及以上学段的学生或数学爱好者，用于直观理解四色定理的几何表述，也可作为图论入门或离散数学教学的辅助工具，帮助学习者观察不同区域邻接关系与颜色分配策略。

GeoGebra 命令及参数

Polygon(A, D, C, B) → p01, a, d, c, b
Polygon(I, H, E, F, G, A) → p02, i, h, e, f, g, a_1
Point(i) → P
Point(d) → S
Polygon(P, Q, R, S, D, I) → p99, p, q, r, s, d_1, i_1
Point(e) → N
Polygon(N, O, M, L) → p05, n_{20}, o, m, l
Polygon(N, O, J, K, H, E) → p04, n_1, o_1, j, k, h_1, e_1
Point(k) → T
Point(q) → W
Polygon(P, T, U, V, W, Q) → p104, p_1, t, u, v, w, q_1
Point(o) → Z
Point(o_1) → B_1
Polygon(Z, A_1, C_1, B_1) → p08, z_1, a_2, c_1, b_1
Polygon(B_1, C_1, D_1, E_1, K, J) → p07, b_2, c_2, d_2, e_2, k_1, j_1
Point(e_2) → F_1
Point(u) → G_1
Polygon(T, F_1, H_1, I_1, G_1, U) → p107, t_1, f_1, h_2, i_2, g_1, u_1
Polygon(W, V, J_1, K_1) → p14, w_1, v_1, j_2, k_2
Point(v_1) → M_1
Polygon(G_1, I_1, L_1, M_1) → p15, g_2, i_3, l_1, m_1
Point(a_2) → Q_1
Polygon(N_1, Q_1, P_1, O_1) → p13, n_2, q_2, p_2, o_2
Point(c_2) → R_1
Polygon(R_1, S_1, P_1, Q_1) → p12, r_1, s_1, p_3, q_3
Polygon(R_1, S_1, T_1, U_1, E_1, D_1) → p11, r_2, s_2, t_2, u_2, e_3, d_3
Point(p_2) → V_1
Polygon(V_1, W_1, Z_1, A_2) → p18, v_2, w_2, z_2, a_3
Point(s_2) → B_2
Polygon(B_2, C_2, Z_1, A_2) → p20, b_3, c_3, z_3, a_4
Polygon(B_2, C_2, D_2, E_2, U_1, T_1) → p83, b_4, c_4, d_4, e_4, u_3, t_3
Point(w_2) → F_2
Polygon(I_2, H_2, G_2, F_2) → p22, i_4, h_3, g_3, f_2
Point(c_3) → N_2
Polygon(F_2, G_2, J_2, N_2) → p23, f_3, g_4, j_3, n_3
Point(c_4) → O_2
Polygon(N_2, J_2, K_2, O_2) → p25, n_4, j_4, k_3, o_3
Polygon(O_2, K_2, L_2, M_2, E_2, D_2) → p85, o_4, k_4, l_2, m_2, e_5, d_5
Point(h_3) → P_2
Point(g_4) → S_2
Polygon(P_2, Q_2, R_2, S_2) → p27, p_4, q_4, r_3, s_3
Point(j_4) → U_2
Polygon(S_2, R_2, T_2, U_2) → p29, s_4, r_4, t_4, u_4
Point(k_4) → W_2
Polygon(U_2, T_2, V_2, W_2) → p31, u_5, t_5, v_3, w_3
Polygon(W_2, V_2, Z_2, A_3, M_2, L_2) → p87, w_4, v_4, z_4, a_5, m_3, l_3
Point(q_4) → B_3
Polygon(B_3, C_3, D_3, E_3) → p33, b_5, c_5, d_6, e_6
Point(r_4) → F_3
Polygon(F_3, G_3, C_3, B_3) → p34, f_4, g_5, c_6, b_6
Point(t_5) → H_3
Polygon(H_3, I_3, G_3, F_3) → p36, h_4, i_5, g_6, f_5
Point(v_4) → J_3
Polygon(J_3, K_3, I_3, H_3) → p38, j_5, k_5, i_6, h_5
Polygon(J_3, K_3, L_3, M_3, A_3, Z_2) → p89, j_6, k_6, l_4, m_4, a_6, z_5
Point(c_5) → N_3
Point(g_5) → Q_3
Polygon(N_3, O_3, P_3, Q_3) → p40, n_5, o_5, p_5, q_5
Point(i_5) → S_3
Polygon(Q_3, P_3, R_3, S_3) → p42, q_6, p_6, r_5, s_5
Point(k_5) → U_3
Polygon(S_3, R_3, T_3, U_3) → p44, s_6, r_6, t_6, u_6
Point(k_6) → W_3
Polygon(U_3, T_3, V_3, W_3) → p46, u_7, t_7, v_5, w_5
Line(G, S) → f_6
Mirror(W_3, f_6) → B_4
Mirror(V_3, f_6) → C_4
Mirror(Z_3, f_6) → D_4
Mirror(M_3, f_6) → F_4
Mirror(L_3, f_6) → G_4
Mirror(U_3, f_6) → H_4
Mirror(T_3, f_6) → I_4
Mirror(V_3, f_6) → J_4
Mirror(W_3, f_6) → K_4
Polygon(H_4, I_4, J_4, K_4) → p47, h_6, i_7, j_7, k_7
Mirror(S_3, f_6) → L_4
Mirror(R_3, f_6) → M_4
Mirror(T_3, f_6) → N_4
Mirror(U_3, f_6) → O_4
Polygon(L_4, M_4, N_4, O_4) → p45, l_6, m_6, n_6, o_6
Mirror(Q_3, f_6) → P_4
Mirror(P_3, f_6) → Q_4
Mirror(R_3, f_6) → R_4
Mirror(S_3, f_6) → S_4
Polygon(P_4, Q_4, R_4, S_4) → p43, p_7, q_7, r_7, s_7
Mirror(N_3, f_6) → T_4
Mirror(O_3, f_6) → U_4
Mirror(P_3, f_6) → V_4
Mirror(Q_3, f_6) → W_4
Polygon(T_4, U_4, V_4, W_4) → p41, t_8, u_8, v_7, w_7
Mirror(J_3, f_6) → Z_4
Mirror(K_3, f_6) → A_5
Mirror(L_3, f_6) → B_5
Mirror(M_3, f_6) → C_5
Mirror(A_3, f_6) → D_5
Mirror(Z_2, f_6) → E_5
Polygon(Z_4, A_5, B_5, C_5, D_5, E_5) → p90, z_7, a_8, b_8, c_8, d_8, e_8
Mirror(J_3, f_6) → F_5
Mirror(K_3, f_6) → G_5
Mirror(I_3, f_6) → H_5
Mirror(H_3, f_6) → I_5
Polygon(F_5, G_5, H_5, I_5) → p39, f_8, g_8, h_7, i_8
Mirror(S_3, f_6) → J_5
Mirror(H_3, f_6) → K_5
Mirror(I_3, f_6) → L_5
Mirror(G_3, f_6) → M_5
Mirror(F_3, f_6) → N_5
Polygon(K_5, L_5, M_5, N_5) → p37, k_8, l_7, m_7, n_7
Mirror(F_3, f_6) → O_5
Mirror(G_3, f_6) → P_5
Mirror(C_3, f_6) → Q_5
Mirror(B_3, f_6) → R_5
Polygon(O_5, P_5, Q_5, R_5) → p35, o_7, p_8, q_8, r_8
Mirror(W_2, f_6) → S_5
Mirror(V_2, f_6) → T_5
Mirror(Z_2, f_6) → U_5
Mirror(A_3, f_6) → V_5
Mirror(M_2, f_6) → W_5
Mirror(L_2, f_6) → Z_5
Polygon(S_5, T_5, U_5, V_5, W_5, Z_5) → p88, s_8, t_9, u_9, v_8, w_8, z_8
Mirror(U_2, f_6) → A_6
Mirror(T_2, f_6) → B_6
Mirror(V_2, f_6) → C_6
Mirror(W_2, f_6) → D_6
Polygon(A_6, B_6, C_6, D_6) → p32, a_9, b_9, c_9, d_9
Mirror(S_2, f_6) → E_6
Mirror(R_2, f_6) → F_6
Mirror(T_2, f_6) → G_6
Mirror(U_2, f_6) → H_6
Polygon(E_6, F_6, G_6, H_6) → p30, e_9, f_9, g_9, h_8
Mirror(P_2, f_6) → I_6
Mirror(Q_2, f_6) → J_6
Mirror(R_2, f_6) → K_6
Mirror(S_2, f_6) → L_6
Polygon(I_6, J_6, K_6, L_6) → p28, i_9, j_8, k_9, l_8
Mirror(O_2, f_6) → M_6
Mirror(K_2, f_6) → N_6
Mirror(L_2, f_6) → O_6
Mirror(M_2, f_6) → P_6
Mirror(E_2, f_6) → Q_6
Mirror(D_2, f_6) → R_6
Polygon(M_6, N_6, O_6, P_6, Q_6, R_6) → p86, m_8, n_8, o_8, p_9, q_9, r_9
Mirror(N_2, f_6) → S_6
Mirror(J_2, f_6) → T_6
Mirror(K_2, f_6) → U_6
Mirror(O_2, f_6) → V_6
Polygon(S_6, T_6, U_6, V_6) → p26, s_9, t_{10}, u_{10}, v_9
Mirror(F_2, f_6) → W_6
Mirror(G_2, f_6) → Z_6
Mirror(J_2, f_6) → A_7
Mirror(N_2, f_6) → B_7
Polygon(W_6, Z_6, A_7, B_7) → p24, w_9, z_9, a_{10}, b_{10}
Mirror(B_2, f_6) → C_7
Mirror(C_2, f_6) → D_7
Mirror(D_2, f_6) → E_7
Mirror(E_2, f_6) → F_7
Mirror(U_1, f_6) → G_7
Mirror(T_1, f_6) → H_7
Polygon(C_7, D_7, E_7, F_7, G_7, H_7) → p84, c_{10}, d_{10}, e_{10}, f_{10}, g_{10}, h_9
Mirror(B_2, f_6) → I_7
Mirror(C_2, f_6) → J_7
Mirror(Z_1, f_6) → K_7
Mirror(A_2, f_6) → L_7
Polygon(I_7, J_7, K_7, L_7) → p21, i_{10}, j_9, k_{10}, l_9
Mirror(V_1, f_6) → M_7
Mirror(W_1, f_6) → N_7
Mirror(Z_1, f_6) → O_7
Mirror(A_2, f_6) → P_7
Polygon(M_7, N_7, O_7, P_7) → p19, m_9, n_9, o_9, p_{10}
Mirror(R_1, f_6) → Q_7
Mirror(S_1, f_6) → R_7
Mirror(T_1, f_6) → S_7
Mirror(U_1, f_6) → T_7
Mirror(E_1, f_6) → U_7
Mirror(D_1, f_6) → V_7
Polygon(Q_7, R_7, S_7, T_7, U_7, V_7) → p82, q_{10}, r_{10}, s_{10}, t_{11}, u_{11}, v_{10}
Mirror(R_1, f_6) → W_7
Mirror(S_1, f_6) → Z_7
Mirror(P_1, f_6) → A_8
Mirror(Q_1, f_6) → B_8
Polygon(W_7, Z_7, A_8, B_8) → p17, w_{10}, z_{10}, a_{11}, b_{11}
Mirror(B_1, f_6) → C_8
Mirror(C_1, f_6) → D_8
Mirror(D_1, f_6) → E_8
Mirror(E_1, f_6) → F_8
Mirror(K, f_6) → K'
Mirror(J, f_6) → J'
Polygon(C_8, D_8, E_8, F_8, K', J') → p10, c_{11}, d_{11}, e_{11}, f_{11}, k', j'
Mirror(Z, f_6) → Z'
Mirror(A_1, f_6) → G_8
Mirror(C_1, f_6) → H_8
Mirror(B_1, f_6) → I_8
Polygon(Z', G_8, H_8, I_8) → p09, z', g_{11}, h_{10}, i_{11}
Mirror(N, f_6) → N'
Mirror(O, f_6) → O'
Mirror(J, f_6) → J'_1
Mirror(K, f_6) → K'_1
Mirror(H, f_6) → H'
Mirror(E, f_6) → E'
Polygon(N', O', J'_1, K'_1, H', E') → p06, n', o', j'_1, k'_1, h', e'
Mirror(I, f_6) → I'
Mirror(H, f_6) → H'_1
Mirror(E, f_6) → E'_1
Mirror(F, f_6) → F'
Mirror(G, f_6) → G'
Mirror(A, f_6) → A'
Polygon(I', H'_1, E'_1, F', G', A') → p03, i', h'_1, e'_1, f', g', a'
Point(u_2) → J_8
Point(h_2) → M_8
Polygon(J_8, K_8, L_8, M_8, H_1, F_1) → p91, j_{10}, k_{11}, l_{10}, m_{10}, h_{11}, f_{12}
Point(i_3) → O_8
Polygon(L_8, N_8, O_8, M_8) → p48, l_{11}, n_{10}, o_{10}, m_{11}
Polygon(O_8, N_8, P_8, Q_8) → p50, o_{11}, n_{11}, p_{11}, q_{11}
Point(e_4) → R_8
Point(k_{11}) → U_8
Polygon(R_8, S_8, T_8, U_8, K_8, J_8) → p93, r_{11}, s_{11}, t_{12}, u_{12}, k_{12}, j_{11}
Point(l_{11}) → W_8
Polygon(U_8, T_8, V_8, W_8) → p51, u_{13}, t_{13}, v_{11}, w_{11}
Point(f_6) → Z_8
Intersect(f_6, n_{11}) → A_9
Polygon(W_8, V_8, Z_8, A_9) → p53, w_{12}, v_{12}, z_{11}, a_{12}
Point(m_2) → B_9
Point(s_{11}) → E_9
Polygon(B_9, C_9, D_9, E_9, S_8, R_8) → p95, b_{12}, c_{12}, d_{12}, e_{12}, s_{12}, r_{12}
Point(t_{13}) → G_9
Polygon(E_9, D_9, F_9, G_9) → p55, e_{13}, d_{13}, f_{13}, g_{12}
Point(v_{12}) → I_9
Polygon(G_9, F_9, H_9, I_9) → p57, g_{13}, f_{14}, h_{12}, i_{12}
Polygon(I_9, H_9, J_9, K_9) → p59, i_{13}, h_{13}, j_{12}, k_{13}
Point(a_5) → L_9
Point(c_{12}) → O_9
Polygon(L_9, M_9, N_9, O_9, C_9, B_9) → p97, l_{12}, m_{12}, n_{12}, o_{12}, c_{13}, b_{13}
Point(d_{13}) → Q_9
Polygon(O_9, N_9, P_9, Q_9) → p60, o_{13}, n_{13}, p_{12}, q_{12}
Point(f_{14}) → S_9
Polygon(Q_9, P_9, R_9, S_9) → p62, q_{13}, p_{13}, r_{13}, s_{13}
Point(f_6) → T_9
Intersect(f_6, h_{13}) → U_9
Polygon(S_9, R_9, T_9, U_9) → p64, s_{14}, r_{14}, t_{14}, u_{14}
Point(m_4) → V_9
Point(m_{12}) → A_{10}
Polygon(V_9, W_9, Z_9, A_{10}, M_9, L_9) → p101, v_{13}, w_{13}, z_{12}, a_{13}, m_{13}, l_{13}
Point(n_{13}) → C_{10}
Polygon(A_{10}, Z_9, B_{10}, C_{10}) → p66, a_{14}, z_{13}, b_{14}, c_{14}
Point(p_{13}) → E_{10}
Polygon(C_{10}, B_{10}, D_{10}, E_{10}) → p68, c_{15}, b_{15}, d_{14}, e_{14}
Point(r_{14}) → G_{10}
Polygon(E_{10}, D_{10}, F_{10}, G_{10}) → p70, e_{15}, d_{15}, f_{15}, g_{14}
Polygon(G_{10}, F_{10}, H_{10}, I_{10}) → p72, g_{15}, f_{16}, h_{14}, i_{14}
Point(w_{13}) → L_{10}
Polygon(M_3, J_{10}, K_{10}, L_{10}, W_9, V_9) → p103, m_{14}, j_{13}, k_{14}, l_{14}, w_{14}, v_{14}
Point(z_{13}) → N_{10}
Polygon(L_{10}, K_{10}, M_{10}, N_{10}) → p73, l_{15}, k_{15}, m_{15}, n_{14}
Point(b_{15}) → P_{10}
Polygon(N_{10}, M_{10}, O_{10}, P_{10}) → p75, n_{15}, m_{16}, o_{14}, p_{14}
Point(d_{15}) → R_{10}
Polygon(P_{10}, O_{10}, Q_{10}, R_{10}) → p77, p_{15}, o_{15}, q_{14}, r_{15}
Point(f_6) → S_{10}
Intersect(f_6, f_{16}) → T_{10}
Polygon(R_{10}, Q_{10}, S_{10}, T_{10}) → p79, r_{16}, q_{15}, s_{15}, t_{15}
Mirror(V_9, f_6) → U_{10}
Mirror(W_9, f_6) → V_{10}
Mirror(Z_9, f_6) → W_{10}
Mirror(A_{10}, f_6) → Z_{10}
Mirror(M_9, f_6) → A_{11}
Mirror(L_9, f_6) → B_{11}
Polygon(U_{10}, V_{10}, W_{10}, Z_{10}, A_{11}, B_{11}) → p102, u_{15}, v_{15}, w_{15}, z_{14}, a_{15}, b_{16}
Mirror(A_{10}, f_6) → C_{11}
Mirror(Z_9, f_6) → D_{11}
Mirror(B_{10}, f_6) → E_{11}
Mirror(C_{10}, f_6) → F_{11}
Polygon(C_{11}, D_{11}, E_{11}, F_{11}) → p67, c_{16}, d_{16}, e_{16}, f_{17}
Mirror(C_{10}, f_6) → G_{11}
Mirror(B_{10}, f_6) → H_{11}
Mirror(D_{10}, f_6) → I_{11}
Mirror(E_{10}, f_6) → J_{11}
Polygon(G_{11}, H_{11}, I_{11}, J_{11}) → p69, g_{16}, h_{15}, i_{15}, j_{14}
Mirror(E_{10}, f_6) → K_{11}
Mirror(D_{10}, f_6) → L_{11}
Mirror(F_{10}, f_6) → M_{11}
Mirror(G_{10}, f_6) → N_{11}
Polygon(K_{11}, L_{11}, M_{11}, N_{11}) → p71, k_{16}, l_{16}, m_{17}, n_{16}
Mirror(L_9, f_6) → O_{11}
Mirror(M_9, f_6) → P_{11}
Mirror(N_9, f_6) → Q_{11}
Mirror(O_9, f_6) → R_{11}
Mirror(C_9, f_6) → S_{11}
Mirror(B_9, f_6) → T_{11}
Polygon(O_{11}, P_{11}, Q_{11}, R_{11}, S_{11}, T_{11}) → p98, o_{16}, p_{16}, q_{16}, r_{17}, s_{16}, t_{16}
Mirror(B_9, f_6) → U_{11}
Mirror(C_9, f_6) → V_{11}
Mirror(D_9, f_6) → W_{11}
Mirror(E_9, f_6) → Z_{11}
Mirror(S_8, f_6) → A_{12}
Mirror(R_8, f_6) → B_{12}
Polygon(U_{11}, V_{11}, W_{11}, Z_{11}, A_{12}, B_{12}) → p96, u_{16}, v_{16}, w_{16}, z_{15}, a_{16}, b_{17}
Mirror(R_8, f_6) → C_{12}
Mirror(S_8, f_6) → D_{12}
Mirror(T_8, f_6) → E_{12}
Mirror(U_8, f_6) → F_{12}
Mirror(K_8, f_6) → G_{12}
Mirror(J_8, f_6) → H_{12}
Polygon(C_{12}, D_{12}, E_{12}, F_{12}, G_{12}, H_{12}) → p94, c_{17}, d_{17}, e_{17}, f_{18}, g_{17}, h_{16}
Mirror(J_8, f_6) → I_{12}
Mirror(K_8, f_6) → J_{12}
Mirror(L_8, f_6) → K_{12}
Mirror(M_8, f_6) → L_{12}
Mirror(H_1, f_6) → M_{12}
Mirror(F_1, f_6) → N_{12}
Polygon(I_{12}, J_{12}, K_{12}, L_{12}, M_{12}, N_{12}) → p92, i_{16}, j_{15}, k_{17}, l_{17}, m_{18}, n_{17}
Mirror(T, f_6) → T'
Mirror(F_1, f_6) → O_{12}
Mirror(H_1, f_6) → P_{12}
Mirror(I_1, f_6) → Q_{12}
Mirror(G_1, f_6) → R_{12}
Mirror(U, f_6) → U'
Polygon(T', O_{12}, P_{12}, Q_{12}, R_{12}, U') → p108, t', o_{17}, p_{17}, q_{17}, r_{18}, u'
Mirror(P, f_6) → P'
Mirror(T, f_6) → T'_1
Mirror(U, f_6) → U'_1
Mirror(V, f_6) → V'
Mirror(W, f_6) → W'
Mirror(Q, f_6) → Q'
Polygon(P', T'_1, U'_1, V', W', Q') → p105, p', t'_1, u'_1, v', w', q'
Mirror(P, f_6) → P'_1
Mirror(Q, f_6) → Q'_1
Mirror(R, f_6) → R'
Mirror(S, f_6) → S'
Mirror(D, f_6) → D'
Mirror(I, f_6) → I'_1
Polygon(P'_1, Q'_1, R', S', D', I'_1) → p100, p'_1, q'_1, r', s', d', i'_1
Mirror(G_1, f_6) → S_{12}
Mirror(I_1, f_6) → T_{12}
Mirror(L_1, f_6) → U_{12}
Mirror(M_1, f_6) → V_{12}
Polygon(S_{12}, T_{12}, U_{12}, V_{12}) → p16, s_{17}, t_{17}, u_{17}, v_{17}
Mirror(L_8, f_6) → W_{12}
Mirror(N_8, f_6) → Z_{12}
Mirror(O_8, f_6) → A_{13}
Mirror(M_8, f_6) → B_{13}
Polygon(W_{12}, Z_{12}, A_{13}, B_{13}) → p49, w_{17}, z_{16}, a_{17}, b_{18}
Mirror(W_8, f_6) → C_{13}
Mirror(V_8, f_6) → D_{13}
Mirror(Z_8, f_6) → E_{13}
Mirror(A_9, f_6) → F_{13}
Polygon(C_{13}, D_{13}, E_{13}, F_{13}) → p54, c_{18}, d_{18}, e_{18}, f_{19}
Mirror(U_8, f_6) → G_{13}
Mirror(T_8, f_6) → H_{13}
Mirror(V_8, f_6) → I_{13}
Mirror(W_8, f_6) → J_{13}
Polygon(G_{13}, H_{13}, I_{13}, J_{13}) → p52, g_{18}, h_{17}, i_{17}, j_{16}
Mirror(G_9, f_6) → K_{13}
Mirror(F_9, f_6) → L_{13}
Mirror(H_9, f_6) → M_{13}
Mirror(I_9, f_6) → N_{13}
Polygon(K_{13}, L_{13}, M_{13}, N_{13}) → p58, k_{18}, l_{18}, m_{19}, n_{18}
Mirror(E_9, f_6) → O_{13}
Mirror(D_9, f_6) → P_{13}
Mirror(F_9, f_6) → Q_{13}
Mirror(G_9, f_6) → R_{13}
Polygon(O_{13}, P_{13}, Q_{13}, R_{13}) → p56, o_{18}, p_{18}, q_{18}, r_{19}
Mirror(S_9, f_6) → S_{13}
Mirror(R_9, f_6) → T_{13}
Mirror(T_9, f_6) → U_{13}
Mirror(U_9, f_6) → V_{13}
Polygon(S_{13}, T_{13}, U_{13}, V_{13}) → p65, s_{18}, t_{18}, u_{18}, v_{18}
Mirror(Q_9, f_6) → W_{13}
Mirror(P_9, f_6) → Z_{13}
Mirror(R_9, f_6) → A_{14}
Mirror(S_9, f_6) → B_{14}
Polygon(W_{13}, Z_{13}, A_{14}, B_{14}) → p63, w_{18}, z_{17}, a_{18}, b_{19}
Mirror(O_9, f_6) → C_{14}
Mirror(N_9, f_6) → D_{14}
Mirror(P_9, f_6) → E_{14}
Mirror(Q_9, f_6) → F_{14}
Polygon(C_{14}, D_{14}, E_{14}, F_{14}) → p61, c_{19}, d_{19}, e_{19}, f_{20}
Mirror(R_{10}, f_6) → G_{14}
Mirror(Q_{10}, f_6) → H_{14}
Mirror(S_{10}, f_6) → I_{14}
Mirror(T_{10}, f_6) → J_{14}
Polygon(G_{14}, H_{14}, I_{14}, J_{14}) → p80, g_{19}, h_{18}, i_{18}, j_{17}
Mirror(P_{10}, f_6) → K_{14}
Mirror(O_{10}, f_6) → L_{14}
Mirror(Q_{10}, f_6) → M_{14}
Mirror(R_{10}, f_6) → N_{14}
Polygon(K_{14}, L_{14}, M_{14}, N_{14}) → p78, k_{19}, l_{19}, m_{20}, n_{19}
Mirror(N_{10}, f_6) → O_{14}
Mirror(M_{10}, f_6) → P_{14}
Mirror(O_{10}, f_6) → Q_{14}
Mirror(P_{10}, f_6) → R_{14}
Polygon(O_{14}, P_{14}, Q_{14}, R_{14}) → p76, o_{19}, p_{19}, q_{19}, r_{20}
Mirror(L_{10}, f_6) → S_{14}
Mirror(K_{10}, f_6) → T_{14}
Mirror(M_{10}, f_6) → U_{14}
Mirror(N_{10}, f_6) → V_{14}
Polygon(S_{14}, T_{14}, U_{14}, V_{14}) → p74, s_{19}, t_{19}, u_{19}, v_{19}
Point(h_{18}) → W_{14}
Polygon(W_3, V_3, Z_3, A_4, E_4, W_{14}, J_{10}, L_3) → p109, w_6, v_6, z_6, a_7, e_7, w_{19}, j_{18}, l_5
Polygon(B_4, C_4, D_4, Z_{14}, F_4, G_4) → p106, b_7, c_7, d_7, z_{18}, f_7, g_7
Polygon(Z_3, A_{15}, B_{15}, C_{15}, T_{14}, S_{14}, V_{10}, U_{10}, Z_{14}, D_4) → p110, z_{19}, d_{20}, a_{19}, b_{20}, c_{20}, t_{20}, s_{20}, v_{20}, u_{20}, z_{20}
Polygon(W_{14}, E_4, D_{15}, C_{15}) → p81, w_{20}, e_{20}, d_{21}, c_{21}
Sum(regiones) → sumaRegiones
Min(regiones) → mínimoRegiones
KeepIf(x ≟ 0, diferencias) → ceros
Length(ceros) → coincidencias

AI 绘图提示语参考

绘制一个平面地图，包含多个相邻区域，用四种颜色着色，确保相邻区域颜色不同。先创建几个基础多边形代表区域，然后用点和线定义边界，通过镜像和交点生成复杂的相邻关系，最后用颜色工具确保每个相邻区域颜色不同，展示四色定理。

以上提示语为根据原始绘图命令整理而来，仅供参考。