毕达哥拉斯树
几何画板及绘图内容加载中,请稍等……
①本范例演示了毕达哥拉斯树这一分形几何图形的构造与生长过程;②涉及的核心数学概念包括勾股定理、多边形构造、矩阵变换、三角函数等;③作图要点提炼自构造摘要,使用了Polygon命令创建多边形,以及A, B, poly1, f, g, h, i, C, D, q1, q2, t1, α, E, q3, q4, t2, F, H, I, J, K, q5, q6, t3, L, M, N, O, P, q7, q8, t4, Q, R, S, T, U, q9, q10等对象进行复杂几何变换;④适合高中及以上数学学习者,用于理解分形几何、矩阵变换及动态几何绘图。
GeoGebra 命令及参数
Polygon(A, B, 4) → poly1, f, g, h, i, C, Dpytha(D, C, α) → E, q3, q4, t2, F, H, I, Jpytha(E, J, α) → K, q5, q6, t3, L, M, N, Opytha(I, H, α) → P, q7, q8, t4, Q, R, S, Tpytha(K, O, α) → U, q9, q10, t5, V, W, Z, A_1pytha(N, M, α) → B_1, q11, q12, t6, C_1, D_1, E_1, F_1pytha(P, T, α) → G_1, q13, q14, t7, H_1, I_1, J_1, K_1pytha(S, R, α) → L_1, q15, q16, t8, M_1, N_1, O_1, P_1pytha(U, A_1, α) → G, q17, q18, t9, Q_1, R_1, S_1, T_1pytha(Z, W, α) → U_1, q19, q20, t10, V_1, W_1, Z_1, A_2pytha(B_1, F_1, α) → B_2, q21, q22, t11, C_2, D_2, E_2, F_2pytha(E_1, D_1, α) → G_2, q23, q24, t12, H_2, I_2, J_2, K_2pytha(G_1, K_1, α) → L_2, q25, q26, t13, M_2, N_2, O_2, P_2pytha(J_1, I_1, α) → Q_2, q27, q28, t14, R_2, S_2, T_2, U_2pytha(L_1, P_1, α) → V_2, q29, q30, t15, W_2, Z_2, A_3, B_3pytha(O_1, N_1, α) → C_3, q31, q32, t16, D_3, E_3, F_3, G_3pytha(V_2, B_3, 45°) → H_3, q33, q34, t17, I_3, J_3, K_3, L_3pytha(A_3, Z_2, 45°) → M_3, q35, q36, t18, N_3, O_3, P_3, Q_3pytha(C_3, G_3, 45°) → R_3, q37, q38, t19, S_3, T_3, U_3, V_3pytha(F_3, E_3, 45°) → W_3, q39, q40, t20, Z_3, A_4, B_4, C_4pytha(G, T_1, 45°) → D_4, q41, q42, t21, E_4, F_4, G_4, H_4pytha(S_1, R_1, 45°) → I_4, q43, q44, t22, J_4, K_4, L_4, M_4pytha(U_1, A_2, 45°) → N_4, q45, q46, t23, O_4, P_4, Q_4, R_4pytha(Z_1, W_1, 45°) → S_4, q47, q48, t24, T_4, U_4, V_4, W_4pytha(B_2, F_2, 45°) → Z_4, q49, q50, t25, A_5, B_5, C_5, D_5pytha(E_2, D_2, 45°) → E_5, q51, q52, t26, F_5, G_5, H_5, I_5pytha(G_2, K_2, 45°) → J_5, q53, q54, t27, K_5, L_5, M_5, N_5pytha(T_2, S_2, 45°) → T_5, q57, q58, t29, U_5, V_5, W_5, Z_5pytha(Q_2, U_2, 45°) → A_6, q59, q60, t30, B_6, C_6, D_6, E_6pytha(O_2, N_2, 45°) → F_6, q61, q62, t31, G_6, H_6, I_6, J_6pytha(L_2, P_2, 45°) → K_6, q63, q64, t32, L_6, M_6, N_6, O_6pytha(J_2, I_2, 45°) → O_5, q55, q56, t28, P_5, Q_5, R_5, S_5
AI 绘图提示语参考
绘制一个由多个直角三角形组成的分形树,每个三角形的直角边与前一个三角形的斜边重合,角度为45度。首先绘制一个直角三角形,然后以该三角形的直角顶点为起点,依次绘制新的直角三角形,每次旋转45度,直到形成复杂的分形结构。
以上提示语为根据原始绘图命令整理而来,仅供参考。