积极 AI Logo 积极 AI

绘制黄金矩形：几何与比例的数学之美

绘制黄金矩形：几何与比例的数学之美
几何画板及绘图内容加载中，请稍等……
2018-08-16 02:11
几何作图函数图像
黄金矩形是数学中一个重要的几何图形，其长宽比为黄金比例（约1.618）。本范例通过GeoGebra演示如何绘制黄金矩形，展示比例关系与几何构造。核心数学概念包括比例、黄金分割和几何作图。作图要点包括使用Point、Polygon、CircleArc等命令，以及通过参数控制图形。适合初中生及以上学习者，用于理解几何比例和图形构造。

GeoGebra 命令及参数

  1. Point(Circle[A, f]) → B
  2. Polygon(A, B, C, D) → poly1, a, b, c, d
  3. Polygon(Corner[1], (x(Corner[1]) + (0.3 * Distance[Corner[1], Corner[2]]), y(Corner[1])), (x(Corner[4]) + (0.3 * Distance[Corner[1], Corner[2]]), y(Corner[4])), Corner[4]) → poly10, i_2, j_2, k_2, l_2
  4. First(Fibonacci, n + 1) → list1
  5. Element(list1, n - 1) → last
  6. Element(list1, n) → beforeLast
  7. Polygon((-22, 3), (-22, 4), (-21, 4), (-21, 3)) → poly2, g, h, i, j
  8. CircleArc((-21, 3), (-21, 4), (-22, 3)) → e
  9. Polygon((-21, 3), (-20, 3), (-20, 4), (-21, 4)) → poly3, l, m, p, q
  10. CircleArc((-21, 3), (-20, 3), (-21, 4)) → k
  11. Polygon((-22, 3), (-22, 1), (-20, 1), (-20, 3)) → poly4, s, t, a_1, b_1
  12. CircleArc((-22, 3), (-22, 1), (-20, 3)) → r
  13. Polygon((-22, 4), (-25, 4), (-25, 1), (-22, 1)) → poly5, d_1, e_1, f_1, g_1
  14. CircleArc((-22, 4), (-25, 4), (-22, 1)) → c_1
  15. Polygon((-20, 4), (-20, 9), (-25, 9), (-25, 4)) → poly6, i_1, j_1, k_1, l_1
  16. CircleArc((-20, 4), (-20, 9), (-25, 4)) → h_1
  17. Polygon((-20, 1), (-12, 1), (-12, 9), (-20, 9)) → poly7, m_1, n_1, q_1, r_1
  18. CircleArc((-20, 1), (-12, 1), (-20, 9)) → p_1
  19. Polygon((-25, 1), (-25, -12), (-12, -12), (-12, 1)) → poly8, t_1, a_2, b_2, c_2
  20. CircleArc((-25, 1), (-25, -12), (-12, 1)) → s_1