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Comparison of A, B, and C Series Paper Ratios

Comparison of A, B, and C Series Paper Ratios
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2020-08-02 15:19
This example demonstrates the size ratio relationships and area comparisons among A, B, and C series paper sizes. It involves core mathematical concepts such as ratios, area calculations, geometric mean, sequences, and functions. GeoGebra commands like IterationList, Sequence, Intersect, Polygon, Line, PointIn, and Segment are used in the construction. Suitable for high school mathematics education to understand geometric shapes and function applications.

GeoGebra Commands & Parameters

  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