边玩边学数学：MathLego

几何画板及绘图内容加载中，请稍等……

2020-03-10 16:01

①本范例通过交互式操作演示多边形、圆形及其交点等几何图形的构建与变化；②涉及的核心数学概念包括算术、微积分、分数、二项分布、集合论、条形图、方差、二次方程等；③作图要点提炼自GeoGebra命令：Polygon（多边形）、Circle（圆）、Intersect（交点）、Sequence（数列）；④适合初中及以上学生及数学爱好者用于几何直观理解与概念学习。

GeoGebra 命令及参数

Polygon(A_2, B, C, D) → poly1, a, b, c, d
Polygon(E, F, 4) → poly2, f, g, h, i, G, H
Circle(I, 0.3) → k
Circle(J, 0.3) → p
Circle(L, 0.3) → q
Circle(K, 0.3) → r_6
Circle(K, 0.3) → s
Circle(L, 0.3) → t
Circle(I, 0.3) → c_1
Circle(J, 0.3) → d_1
Polygon(E_4, F_1, 4) → poly2_1, f_1, g_1, h_1, i_1, G_1, H_1
Circle(I_1, 0.3) → k_1
Circle(J_1, 0.3) → p_1
Circle(L_1, 0.3) → q_1
Circle(K_1, 0.3) → r_1
Circle(K_1, 0.3) → s_1
Circle(L_1, 0.3) → t_1
Circle(I_1, 0.3) → c_2
Circle(J_1, 0.3) → d_2
Polygon(E_6, F_2, 4) → poly2_2, f_2, g_2, h_2, i_2, G_2, H_2
Circle(I_2, 0.3) → k_2
Circle(J_2, 0.3) → p_2
Circle(L_2, 0.3) → q_2
Circle(K_2, 0.3) → r_2
Circle(K_2, 0.3) → s_2
Circle(L_2, 0.3) → t_2
Circle(I_2, 0.3) → c_3
Circle(J_2, 0.3) → d_3
Polygon(E_7, F_3, 4) → poly2_3, f_3, g_3, h_3, i_3, G_3, H_3
Circle(I_3, 0.3) → k_3
Circle(J_3, 0.3) → p_3
Circle(L_3, 0.3) → q_3
Circle(K_3, 0.3) → r_3
Circle(K_3, 0.3) → s_3
Circle(L_3, 0.3) → t_3
Circle(I_3, 0.3) → c_4
Circle(J_3, 0.3) → d_4
Polygon(E_8, F_4, 4) → poly2_4, f_4, g_4, h_4, i_4, G_4, H_4
Circle(I_4, 0.3) → k_4
Circle(J_4, 0.3) → p_4
Circle(L_4, 0.3) → q_4
Circle(K_4, 0.3) → r_4
Circle(K_4, 0.3) → s_4
Circle(L_4, 0.3) → t_4
Circle(I_4, 0.3) → c_5
Circle(J_4, 0.3) → d_5
Polygon(E_9, F_5, 4) → poly2_5, f_5, g_5, h_5, i_5, G_5, H_5
Circle(I_5, 0.3) → k_5
Circle(J_5, 0.3) → p_5
Circle(L_5, 0.3) → q_5
Circle(K_5, 0.3) → r_5
Circle(K_5, 0.3) → s_5
Circle(L_5, 0.3) → t_5
Circle(I_5, 0.3) → c_6
Circle(J_5, 0.3) → d_6
Polygon(O, P, N, M_5) → poly3, o, p_6, n, m
Circle(U, 0.3) → e_1
Circle(V, 0.3) → e_2
Circle(W, 0.3) → e_3
Circle(Z, 0.3) → e_4
Circle(Q, 0.3) → e_5
Circle(R, 0.3) → e_6
Circle(S_5, 0.3) → f_6
Circle(T, 0.3) → g_6
Polygon(O_1, P_3, N_1, M_1) → poly3_1, o_1, p_7, n_1, m_1
Circle(U_1, 0.3) → e_7
Circle(V_1, 0.3) → e_8
Circle(W_1, 0.3) → e_9
Circle(Z_1, 0.3) → e_{10}
Circle(Q_1, 0.3) → e_{11}
Circle(R_1, 0.3) → e_{12}
Circle(S_1, 0.3) → f_7
Circle(T_1, 0.3) → g_7
Polygon(O_2, P_5, N_2, M_2) → poly3_2, o_2, p_8, n_2, m_2
Circle(U_2, 0.3) → e_{13}
Circle(V_2, 0.3) → e_{14}
Circle(W_2, 0.3) → e_{15}
Circle(Z_2, 0.3) → e_{16}
Circle(Q_2, 0.3) → e_{17}
Circle(R_2, 0.3) → e_{18}
Circle(S_2, 0.3) → f_8
Circle(T_2, 0.3) → g_8
Polygon(O_3, P_6, N_3, M_3) → poly3_3, o_3, p_9, n_3, m_3
Circle(U_3, 0.3) → e_{19}
Circle(V_3, 0.3) → e_{20}
Circle(W_3, 0.3) → e_{21}
Circle(Z_3, 0.3) → e_{22}
Circle(Q_3, 0.3) → e_{23}
Circle(R_3, 0.3) → e_{24}
Circle(S_3, 0.3) → f_9
Circle(T_3, 0.3) → g_9
Polygon(B_3, C_2, A_3, A_4) → poly4_1, b_2, c_8, a_5, a_4
Circle(D_2, 0.3) → h_7
Circle(B_4, 0.3) → k_7
Polygon(B_5, C_3, A_5, A_6) → poly4_2, b_3, c_9, a_7, a_6
Circle(D_3, 0.3) → h_8
Circle(B_6, 0.3) → k_8
Polygon(B_7, C_4, A_7, A_8) → poly4_3, b_4, c_{10}, a_9, a_8
Circle(D_4, 0.3) → h_9
Circle(B_8, 0.3) → k_9
Polygon(B_9, C_5, A_9, A_{10}) → poly4_4, b_5, c_{11}, a_{11}, a_{10}
Circle(D_5, 0.3) → h_{10}
Circle(B_{10}, 0.3) → k_{10}
Polygon(B_{11}, C_6, A_{11}, A_{12}) → poly4_5, b_6, c_{12}, a_{13}, a_{12}
Circle(D_6, 0.3) → h_{11}
Circle(B_{12}, 0.3) → k_{11}
Polygon(B_{13}, C_7, A_{13}, A_{14}) → poly4_6, b_7, c_{13}, a_{15}, a_{14}
Circle(D_7, 0.3) → h_{12}
Circle(B_{14}, 0.3) → k_{12}
Polygon(B_{15}, C_8, A_{15}, A_{16}) → poly4_7, b_8, c_{14}, a_{17}, a_{16}
Circle(D_8, 0.3) → h_{13}
Circle(B_{16}, 0.3) → k_{13}
Polygon(B_{17}, C_9, A_{17}, A_{18}) → poly4_8, b_9, c_{15}, a_{19}, a_{18}
Circle(D_9, 0.3) → h_{14}
Circle(B_{18}, 0.3) → k_{14}
Polygon(N_4, O_4, M_4, M) → poly4, n_4, o_4, m_4, m_5
Circle(Q_4, 0.3) → h_6
Polygon(N_5, O_5, M_6, M_7) → poly4_9, n_5, o_5, m_7, m_6
Circle(Q_5, 0.3) → h_{15}
Polygon(N_6, O_6, M_8, M_9) → poly4_{10}, n_6, o_6, m_9, m_8
Circle(Q_6, 0.3) → h_{16}
Polygon(N_7, O_7, M_{10}, M_{11}) → poly4_{11}, n_7, o_7, m_{11}, m_{10}
Circle(Q_7, 0.3) → h_{17}
Polygon(N_8, O_8, M_{12}, M_{13}) → poly4_{12}, n_8, o_8, m_{13}, m_{12}
Circle(Q_8, 0.3) → h_{18}
Polygon(N_9, O_9, M_{14}, M_{15}) → poly4_{13}, n_9, o_9, m_{15}, m_{14}
Circle(Q_9, 0.3) → h_{19}
Polygon(N_{10}, O_{10}, M_{16}, M_{17}) → poly4_{14}, n_{10}, o_{10}, m_{17}, m_{16}
Circle(Q_{10}, 0.3) → h_{20}
Polygon(N_{11}, O_{11}, M_{18}, M_{19}) → poly4_{15}, n_{11}, o_{11}, m_{19}, m_{18}
Circle(Q_{11}, 0.3) → h_{21}
Polygon(N_{12}, O_{12}, M_{20}, M_{21}) → poly4_{16}, n_{12}, o_{12}, m_{21}, m_{20}
Circle(Q_{12}, 0.3) → h_{22}
Polygon(N_{13}, O_{13}, M_{22}, M_{23}) → poly4_{17}, n_{13}, o_{13}, m_{23}, m_{22}
Circle(Q_{13}, 0.3) → h_{23}
Intersect(m_5, m_4) → R_4
Polygon(T_4, U_4, S_4, S) → poly5, t_6, u_4, s_6, s_7
Sequence(S + (i, 0.5), i, 0.5, 7.5) → liste2
Sequence(S + (i, 1.5), i, 0.5, 7.5) → liste3
Sequence(Circle[Element[liste2, i], 0.3], i, 1, Length[liste2]) → liste4
Sequence(Circle[Element[liste3, i], 0.3], i, 1, Length[liste3]) → liste5
Polygon(T_5, U_5, S_6, S_7) → poly5_1, t_7, u_1, s_9, s_8
Sequence(S_7 + (i, 0.5), i, 0.5, 7.5) → liste2_1
Sequence(S_7 + (i, 1.5), i, 0.5, 7.5) → liste3_1
Sequence(Circle[Element[liste2_1, i], 0.3], i, 1, Length[liste2_1]) → liste4_1
Sequence(Circle[Element[liste3_1, i], 0.3], i, 1, Length[liste3_1]) → liste5_1
Polygon(T_6, U_6, S_8, S_9) → poly5_2, t_8, u_2, s_{11}, s_{10}
Sequence(S_9 + (i, 0.5), i, 0.5, 7.5) → liste2_2
Sequence(S_9 + (i, 1.5), i, 0.5, 7.5) → liste3_2
Sequence(Circle[Element[liste2_2, i], 0.3], i, 1, Length[liste2_2]) → liste4_2
Sequence(Circle[Element[liste3_2, i], 0.3], i, 1, Length[liste3_2]) → liste5_2
Sequence(Sequence[Circle[(i, j), 0.3], i, 1, 15], j, 1, 14) → plaque
Sequence(Sequence[Circle[(i, j), 0.3], i, 1, 15], j, 1, 14) → liste1

AI 绘图提示语参考

画一个由多个正方形和圆形组成的几何图形，正方形数量较多，每个正方形内部和外部都绘制了若干个半径为0.3的圆形，这些圆形之间有部分重叠，整体呈现出复杂的几何图案，适合用于数学教学和几何原理可视化。

以上提示语为根据原始绘图命令整理而来，仅供参考。