无平方的勾股定理演示

无平方的勾股定理演示
几何画板及绘图内容加载中,请稍等……
2014-11-05 23:21
①本范例通过动态演示,展示勾股定理的一个直观扩展,不涉及平方计算;②核心数学概念包括直角三角形、距离公式、向量运算;③作图要点使用了GeoGebra命令:Segment(线段)、OrthogonalLine(垂线)、Point(点)、Polygon(多边形)、Angle(角度);④适合高中数学教学,用于理解勾股定理的几何意义和向量表示。

GeoGebra 命令及参数

  1. Segment(A, B) → a
  2. OrthogonalLine(B, a) → b
  3. Point(b) → C
  4. Segment(C, B) → c
  5. Segment(C, A) → d
  6. Polygon(A, C, n) → poly1, e, n_1, b_{16}, D, E, J, M, P, S, V, A_1, D_1, r_1, G_1, J_1, M_1, P_1, S_1, V_1, A_2, D_2, G_2, J_2, a_2, M_2, P_2, S_2, V_2, A_3, D_3, G_3, J_3, M_3, P_3, d_2, S_3, V_3, A_4, D_4, G_4, J_4, M_4, P_4, S_4, V_4, g_2, A_5, D_5, G_5, J_5, M_5, P_5, S_5, V_5, A_6, D_6, j_2, G_6, J_6, M_6, P_6, S_6, V_6, A_7, D_7, G_7, J_7, m_2, M_7, P_7, S_7, V_7, A_8, D_8, G_8, J_8, M_8, P_8, q_2, S_8, V_8, A_9, D_9, G_9, J_9, M_9, P_9, S_9, V_9, t_2, A_{10}, D_{10}, G_{10}, J_{10}, M_{10}, P_{10}, S_{10}, V_{10}, A_{11}, D_{11}, c_3, G_{11}, J_{11}, M_{11}, P_{11}, S_{11}, V_{11}, A_{12}, D_{12}, G_{12}, f, f_3, i_3, l_3, p_3, s_3, e_4, h_4, k_4, n_4, r_4, g, a_5, d_5, g_5, j_5, m_5, q_5, t_5, c_6, f_6, i_6, h, l_6, p_6, s_6, b_7, e_7, h_7, k_7, n_7, r_7, a_8, s, d_8, g_8, j_8, m_8, q_8, t_8, c_9, f_9, i_9, l_9, b_1, p_9, s_9, b_{10}, e_{10}, h_{10}, k_{10}, n_{10}, r_{10}, a_{11}, d_{11}, e_1, g_{11}, j_{11}, m_{11}, q_{11}, t_{11}, c_{12}, f_{12}, i_{12}, l_{12}, p_{12}, h_1, s_{12}, b_{13}, e_{13}, h_{13}, k_{13}, n_{13}, r_{13}, a_{14}, d_{14}, g_{14}, k_1, j_{14}, m_{14}, q_{14}, t_{14}, c_{15}, f_{15}, i_{15}, l_{15}, p_{15}, s_{15}
  7. Polygon(C, B, n) → poly2, i, p_1, c_{16}, F, G, K, N, Q, T, W, B_1, E_1, s_1, H_1, K_1, N_1, Q_1, T_1, W_1, B_2, E_2, H_2, K_2, b_2, N_2, Q_2, T_2, W_2, B_3, E_3, H_3, K_3, N_3, Q_3, e_2, T_3, W_3, B_4, E_4, H_4, K_4, N_4, Q_4, T_4, W_4, h_2, B_5, E_5, H_5, K_5, N_5, Q_5, T_5, W_5, B_6, E_6, k_2, H_6, K_6, N_6, Q_6, T_6, W_6, B_7, E_7, H_7, K_7, n_2, N_7, Q_7, T_7, W_7, B_8, E_8, H_8, K_8, N_8, Q_8, r_2, T_8, W_8, B_9, E_9, H_9, K_9, N_9, Q_9, T_9, W_9, a_3, B_{10}, E_{10}, H_{10}, K_{10}, N_{10}, Q_{10}, T_{10}, W_{10}, B_{11}, E_{11}, d_3, H_{11}, K_{11}, N_{11}, Q_{11}, T_{11}, W_{11}, B_{12}, E_{12}, H_{12}, j, g_3, j_3, m_3, q_3, t_3, f_4, i_4, l_4, p_4, s_4, k, b_5, e_5, h_5, k_5, n_5, r_5, a_6, d_6, g_6, j_6, l, m_6, q_6, t_6, c_7, f_7, i_7, l_7, p_7, s_7, b_8, t, e_8, h_8, k_8, n_8, r_8, a_9, d_9, g_9, j_9, m_9, c_1, q_9, t_9, c_{10}, f_{10}, i_{10}, l_{10}, p_{10}, s_{10}, b_{11}, e_{11}, f_1, h_{11}, k_{11}, n_{11}, r_{11}, a_{12}, d_{12}, g_{12}, j_{12}, m_{12}, q_{12}, i_1, t_{12}, c_{13}, f_{13}, i_{13}, l_{13}, p_{13}, s_{13}, b_{14}, e_{14}, h_{14}, l_1, k_{14}, n_{14}, r_{14}, a_{15}, d_{15}, g_{15}, j_{15}, m_{15}, q_{15}, t_{15}
  8. Polygon(B, A, n) → poly3, m, q_1, d_{16}, H, I, L, O, R, U, Z, C_1, F_1, t_1, I_1, L_1, O_1, R_1, U_1, Z_1, C_2, F_2, I_2, L_2, c_2, O_2, R_2, U_2, Z_2, C_3, F_3, I_3, L_3, O_3, R_3, f_2, U_3, Z_3, C_4, F_4, I_4, L_4, O_4, R_4, U_4, Z_4, i_2, C_5, F_5, I_5, L_5, O_5, R_5, U_5, Z_5, C_6, F_6, l_2, I_6, L_6, O_6, R_6, U_6, Z_6, C_7, F_7, I_7, L_7, p_2, O_7, R_7, U_7, Z_7, C_8, F_8, I_8, L_8, O_8, R_8, s_2, U_8, Z_8, C_9, F_9, I_9, L_9, O_9, R_9, U_9, Z_9, b_3, C_{10}, F_{10}, I_{10}, L_{10}, O_{10}, R_{10}, U_{10}, Z_{10}, C_{11}, F_{11}, e_3, I_{11}, L_{11}, O_{11}, R_{11}, U_{11}, Z_{11}, C_{12}, F_{12}, I_{12}, p, h_3, k_3, n_3, r_3, d_4, g_4, j_4, m_4, q_4, t_4, q, c_5, f_5, i_5, l_5, p_5, s_5, b_6, e_6, h_6, k_6, r, n_6, r_6, a_7, d_7, g_7, j_7, m_7, q_7, t_7, c_8, a_1, f_8, i_8, l_8, p_8, s_8, b_9, e_9, h_9, k_9, n_9, d_1, r_9, a_{10}, d_{10}, g_{10}, j_{10}, m_{10}, q_{10}, t_{10}, c_{11}, f_{11}, g_1, i_{11}, l_{11}, p_{11}, s_{11}, b_{12}, e_{12}, h_{12}, k_{12}, n_{12}, r_{12}, j_1, a_{13}, d_{13}, g_{13}, j_{13}, m_{13}, q_{13}, t_{13}, c_{14}, f_{14}, i_{14}, m_1, l_{14}, p_{14}, s_{14}, b_{15}, e_{15}, h_{15}, k_{15}, n_{15}, r_{15}, a_{16}
  9. Angle(C, B, A) → α
  10. Polygon(A, B, C) → poly4, c_4, a_4, b_4

AI 绘图提示语参考

画一个直角三角形,标出两条直角边和斜边,然后分别以两条直角边为边长向外作正方形,再连接正方形的对角线,展示直角三角形斜边平方等于两条直角边平方和的几何意义,最后用向量表示并展示其关系。
以上提示语为根据原始绘图命令整理而来,仅供参考。