八边形中线构造

八边形中线构造
几何画板及绘图内容加载中,请稍等……
2019-12-31 16:42
①本范例演示八边形中线的几何构造与性质;②涉及核心数学概念包括对称性、多边形构造、中点计算、向量运算;③构造过程中运用了Intersect(交点)、ConstructionStep(构造步骤)、Point(点)、Polygon(多边形)、Midpoint(中点)、Segment(线段)、PolyLine(多段线)、Vector(向量)、Sequence(数列)等GeoGebra命令与对象;④适合高中数学教学,用于理解几何作图与空间关系。

GeoGebra 命令及参数

  1. Intersect(xAxis, yAxis) → A
  2. ConstructionStep() → stap
  3. Point(xAxis) → B
  4. Polygon(A, B, 8) → veelhoek1, f, D, E, F, G, H, g, h, i, j, k, l, m, C
  5. Polygon(D, C, 8) → veelhoek2, n, J, K, L, M, N, p, q, r, s, t, a, b, I
  6. Polygon(L, K, 8) → veelhoek3, c, P, Q, R, S, T, d, e, f_1, g_1, h_1, i_1, j_1, O
  7. Polygon(R, Q, 8) → veelhoek4, k_1, V, W, Z, A_1, B_1, l_1, m_1, n_1, p_1, q_1, r_1, s_1, U
  8. Polygon(B, A, 8) → veelhoek5, t_1, D_1, E_1, F_1, G_1, H_1, a_1, b_1, c_1, d_1, e_1, f_2, g_2, C_1
  9. Polygon(J, I, 8) → veelhoek6, h_2, J_1, K_1, L_1, M_1, N_1, i_2, j_2, k_2, l_2, m_2, n_2, p_2, I_1
  10. Polygon(P, O, 8) → veelhoek7, q_2, P_1, Q_1, R_1, S_1, T_1, r_2, s_2, t_2, a_2, b_2, c_2, d_2, O_1
  11. Polygon(V, U, 8) → veelhoek8, e_2, V_1, W_1, Z_1, A_2, B_2, f_3, g_3, h_3, i_3, j_3, k_3, l_3, U_1
  12. Polygon(F, E, 8) → veelhoek9, m_3, D_2, E_2, F_2, G_2, H_2, n_3, p_3, q_3, r_3, s_3, t_3, a_3, C_2
  13. Polygon(N, M, 8) → veelhoek10, b_3, J_2, K_2, L_2, M_2, N_2, c_3, d_3, e_3, f_4, g_4, h_4, i_4, I_2
  14. Polygon(T, S, 8) → veelhoek11, j_4, P_2, Q_2, R_2, S_2, T_2, k_4, l_4, m_4, n_4, p_4, q_4, r_4, O_2
  15. Polygon(B_1, A_1, 8) → veelhoek12, s_4, V_2, W_2, Z_2, A_3, B_3, t_4, a_4, b_4, c_4, d_4, e_4, f_5, U_2
  16. Midpoint(f) → C_3
  17. Midpoint(g) → D_3
  18. Midpoint(h) → E_3
  19. Midpoint(i) → F_3
  20. Midpoint(j) → G_3
  21. Midpoint(k) → H_3
  22. Midpoint(l) → I_3
  23. Midpoint(m) → J_3
  24. Segment(C_3, E_3) → g_5
  25. Segment(D_3, F_3) → h_5
  26. Segment(E_3, G_3) → i_5
  27. Segment(F_3, H_3) → j_5
  28. Segment(G_3, I_3) → k_5
  29. Segment(H_3, J_3) → l_5
  30. Segment(I_3, C_3) → m_5
  31. Segment(J_3, D_3) → n_5
  32. Intersect(i_5, j_5) → K_3
  33. Intersect(j_5, k_5) → L_3
  34. Intersect(k_5, l_5) → M_3
  35. Intersect(l_5, m_5) → N_3
  36. Segment(C_3, E_3) → p_5
  37. Intersect(m_5, n_5) → O_3
  38. Intersect(n_5, p_5) → P_3
  39. Intersect(h_5, p_5) → Q_3
  40. Intersect(h_5, i_5) → R_3
  41. PolyLine(G_3, L_3, D_3, Q_3, E_3, R_3, F_3, K_3, G_3, H_3, M_3, I_3, N_3, J_3, O_3, C_3, P_3) → q_5
  42. Vector(A, I) → hor
  43. Vector(A, F) → vert
  44. Sequence(Translate[Sequence[PolyLine[Translate[G_3, Vector[(nn * hor)]], Translate[L_3, Vector[(nn * hor)]], Translate[H_3, Vector[(nn * hor)]], Translate[M_3, Vector[(nn * hor)]], Translate[I_3, Vector[(nn * hor)]], Translate[N_3, Vector[(nn * hor)]], Translate[J_3, Vector[(nn * hor)]], Translate[O_3, Vector[(nn * hor)]], Translate[C_3, Vector[(nn * hor)]], Translate[P_3, Vector[(nn * hor)]], Translate[D_3, Vector[(nn * hor)]], Translate[Q_3, Vector[(nn * hor)]], Translate[E_3, Vector[(nn * hor)]], Translate[R_3, Vector[(nn * hor)]], Translate[F_3, Vector[(nn * hor)]], Translate[K_3, Vector[(nn * hor)]], Translate[G_3, Vector[(nn * hor)]]], nn, 0, 3], Vector[(mm * vert)]], mm, -1, 1) → l1
  45. Polygon(B, H_1, I, C) → vierhoek1, b_5, r_5, i_6, c_5
  46. Sequence(Translate[Sequence[Polygon[Translate[B, Vector[(nn * hor)]], Translate[H_1, Vector[(nn * hor)]], Translate[I, Vector[(nn * hor)]], Translate[C, Vector[(nn * hor)]]], nn, 0, 2], Vector[(mm * vert)]], mm, 0, 1) → l2

AI 绘图提示语参考

绘制一个正八边形,并构造其对角线的中点,连接这些中点形成新的八边形。接着,以原八边形的边为底,构造一系列平行四边形,最终形成一个中心对称的图形。
以上提示语为根据原始绘图命令整理而来,仅供参考。