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分数可视化 by John Golden

分数可视化 by John Golden
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2020-03-17 10:12
圆数列概率统计参数方程几何作图
①本范例通过动态演示分数的面积表示，直观展示分数与几何图形的关系；②涉及核心数学概念包括分数、面积、内切圆、外接圆、参数曲线及随机过程；③作图要点运用了RandomElement, Random, Point, Segment, Polygon, Midpoint, Defined, If, Sequence, Translate等GeoGebra命令与对象；④适合初中及以上数学教学，用于辅助理解分数、几何及参数方程。

GeoGebra 命令及参数

  1. RandomElement(l1) → a
  2. RandomElement(l1) → b
  3. Random(1, a) → c
  4. RandomElement(l2) → e
  5. Point(Ray[A, A + (1, 0)]) → B
  6. Segment(A, B) → f
  7. Segment(E, C) → g
  8. Polygon(F, (x(G), y(F)), G, (x(F), y(G))) → q1, f_1, i, g_1, j
  9. Midpoint(g) → H
  10. Defined(IndexOf[D, l3]) → k
  11. If(¬k, Midpoint[I, F], I) → K
  12. If(¬k, F + (2 / D * (J - F)), F + (1 / D * (J - F))) → L
  13. Polygon(F, K, M, L) → q2, f_2, k_1, m, l
  14. Sequence(Polygon[Translate[F, (i * (L - F))], Translate[K, (i * (L - F))], Translate[M, (i * (L - F))], Translate[L, (i * (L - F))]], i, 0, If[k, N, Min[N, D / 2]] - 1) → l4
  15. If((¬k) ∧ N > D / 2, Sequence[Translate[Polygon[Translate[F, K - F], Translate[K, K - F], Translate[M, K - F], Translate[L, K - F]], (i * (L - F))], i, 0, N - D / 2 - 1]) → l5
  16. Point(Ray[O, O + (0, 1)]) → P
  17. Sequence(Rotate[CircleSector[O, P, Rotate[P, (360°) / D, O]], (i * (360°) / D), O], i, 0, N - 1) → l6
  18. Translate({l4, l5}, Q - F) → l7