积极 AI Logo 积极 AI

A、B、C系列纸张比例比较

A、B、C系列纸张比例比较
几何画板及绘图内容加载中，请稍等……
2020-08-02 15:19
①本范例演示了A、B、C系列纸张的尺寸比例关系及面积对比；②涉及核心数学概念包括比例、面积计算、几何平均数、数列与函数；③构造过程中运用了IterationList, Sequence, Intersect, Polygon, Line, PointIn, Segment等GeoGebra命令与对象；④适合高中阶段数学教学，用于理解几何图形与函数应用。

GeoGebra 命令及参数

  1. IterationList({Element[v, 2], Element[v, 1] / 2}, v, {{sqrt(2), 1}}, N) → m2
  2. Sequence((Element[m2, i, 1], Element[m2, i, 2]), i, 1, N + 1) → l2
  3. IterationList({Element[v, 2], Element[v, 1] / 2}, v, {{sqrt(sqrt(2)), 1 / sqrt(sqrt(2))}}, N) → m1
  4. Sequence((Element[m1, i, 1], Element[m1, i, 2]), i, 1, N + 1) → l1
  5. Intersect(xAxis, yAxis) → A
  6. Polygon(A, B, C, D) → q1, b1, a1, c, d
  7. Line(A, A0) → g
  8. PointIn(q1) → Pointq1
  9. Intersect(g, b1) → E
  10. Segment(A, C) → f
  11. Polygon((0, 0), (0, y(A5)), A5, (x(A5), 0)) → A5Rect, h, i, a5, j
  12. Polygon((0, 0), (0, y(A4)), A4, (x(A4), 0)) → A4Rect, k, l, a4, m
  13. Polygon((0, 0), (0, y(A3)), A3, (x(A3), 0)) → A3Rect, n, p, a3, q
  14. Polygon((0, 0), (0, y(A2)), A2, (x(A2), 0)) → A2Rect, r, s, a2, t
  15. Polygon((0, 0), (0, y(A1)), A1, (x(A1), 0)) → A1Rect, a, b, e, f_1
  16. Polygon((0, 0), (0, y(A0)), A0, (x(A0), 0)) → A0Rect, g_1, h_1, a0, i_1
  17. Segment(E, C) → j_1
  18. Polygon((0, 0), (0, y(B0)), B0, (x(B0), 0)) → B0Rect, k_1, l_1, b0, m_1
  19. Polygon((-0.0019494078812289928, 0), (0, y(B1)), B1, (x(B1), 0)) → B1Rect, n_1, p_1, q_1, r_1
  20. Polygon((0, 0), (0, y(B2)), B2, (x(B2), 0)) → B2Rect, s_1, t_1, b2, a_1
  21. Polygon((0, 0), (0, y(B3)), B3, (x(B3), 0)) → B3Rect, b_1, c_1, b3, d_1
  22. Polygon((0, 0), (0, y(B4)), B4, (x(B4), 0)) → B4Rect, e_1, f_2, b4, g_2
  23. Segment(B, E) → h_2
  24. IterationList({Element[v, 2], Element[v, 1] / 2}, v, {{sqrt((sqrt(2) * areaC0)), sqrt(areaC0 / sqrt(2))}}, N) → m3
  25. Sequence((Element[m3, i, 1], Element[m3, i, 2]), i, 1, N + 1) → l3
  26. Sequence(Polygon[A, (x(l3(i)), 0), l3(i), (0, y(l3(i)))], i, 1, N) → l4