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A-Series Paper Ratio Demonstration

A-Series Paper Ratio Demonstration
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2020-08-02 17:32
PolygonSequenceCoordinate Geometry
This example illustrates the dimensional ratio of A-series paper sizes, dynamically visualizing the side length proportions and area changes across different paper sizes. It involves core mathematical concepts such as ratios, sequences, polygon area calculations, and coordinate geometry. GeoGebra commands like IterationList, Sequence, Intersect, Polygon, Line, PointIn, and Segment are used to construct the paper sizes and calculate intersections. Suitable for high school mathematics instruction on ratios, sequences, geometric constructions, and as an extension in solid geometry for paper size analysis.

GeoGebra Commands & Parameters

  1. IterationList({Element[v, 2], Element[v, 1] / 2}, v, {{sqrt(sqrt(2)), 1 / sqrt(sqrt(2))}}, N) → m1
  2. Sequence((Element[m1, i, 1], Element[m1, i, 2]), i, 1, N + 1) → l1
  3. Intersect(xAxis, yAxis) → A
  4. Polygon(A, B, C, D) → q1, b1, a1, c, d
  5. Line(A, A0) → g
  6. PointIn(q1) → Pointq1
  7. Intersect(g, b1) → E
  8. Segment(A, C) → f
  9. Polygon((0, 0), (0, y(A5)), A5, (x(A5), 0)) → A5Rect, h, i, a5, j
  10. Polygon((0, 0), (0, y(A4)), A4, (x(A4), 0)) → A4Rect, k, l, a4, m
  11. Polygon((0, 0), (0, y(A3)), A3, (x(A3), 0)) → A3Rect, n, p, a3, q
  12. Polygon((0, 0), (0, y(A2)), A2, (x(A2), 0)) → A2Rect, r, s, a2, t
  13. Polygon((0, 0), (0, y(A1)), A1, (x(A1), 0)) → A1Rect, a, b, e, f_1
  14. Polygon((0, 0), (0, y(A0)), A0, (x(A0), 0)) → A0Rect, g_1, h_1, a0, i_1
  15. Segment(E, C) → j_1
  16. Segment(B, E) → h_2