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分数除法：a ÷ b（部分法）

分数除法：a ÷ b（部分法）
几何画板及绘图内容加载中，请稍等……
2018-10-21 21:58
几何作图
①本范例演示分数除法a ÷ b在部分法情境下的理解；②核心数学概念为分数除法与部分法除法的等价性，即a ÷ b = a/b；③作图要点使用了Point, Segment, Sequence, Polygon, GCD等GeoGebra命令和对象；④适合初中数学教学，用于帮助学生理解分数除法的几何意义。

GeoGebra 命令及参数

  1. Point(Segment[(x(D) + 2 / 5, y(D)), (x(D) + 1, y(D))]) → S
  2. Segment(A, (x(A) + 1, y(A))) → l1
  3. Point(Segment[(x(A) + 1 / 5, y(A)), (x(A) + 1, y(A))]) → P
  4. Segment(B, (x(B) + 1, y(B))) → l2
  5. Point(Segment[(x(B) + 2 / 6, y(B)), (x(B) + 1, y(B))]) → Q
  6. Point(Segment[(x(C) + 1 / 6 - 0.0050, y(C)), (x(Q) - 1 / 6, y(C))]) → R
  7. Segment(C, (x(C) + 1, y(C))) → l3
  8. Sequence(Circle[(2.5 * (i - 1), 0), 1], i, 1, a) → list1
  9. Sequence(Segment[(2.5 * a, 0), (2.5 * a - sin(j * θ), cos(j * θ))], j, 1, c - 1) → list2
  10. Segment(D, (x(D) + 1, y(D))) → l4
  11. Polygon((-0.5, -3.24), (1, -3.24), (1, -1.24), (-0.5, -1.24)) → poly1, e, g, h, i
  12. GCD(a, d) → k
  13. Segment(A, P) → j
  14. Segment(C, R) → l
  15. Segment(B, Q) → m
  16. Segment(D, S) → n
  17. Point(Segment[(x(A_1) + 1 / 7, y(A_1)), (x(A_1) + 1, y(A_1))]) → P_1
  18. Segment(A_1, P_1) → j_1
  19. Point(Segment[(x(D_1) + 2 / 5, y(D_1)), (x(D_1) + 1, y(D_1))]) → S_1
  20. Point(Segment[(x(A_2) + 1 / 7, y(A_2)), (x(A_2) + 1, y(A_2))]) → P_2
  21. GCD(a_1, d_1) → k_1
  22. Segment(A_2, P_2) → j_2
  23. Segment(D_1, S_1) → n_1
  24. Point(Segment[(x(D_2) + 2 / 5, y(D_2)), (x(D_2) + 1, y(D_2))]) → S_2
  25. Point(Segment[(x(A_3) + 1 / 7, y(A_3)), (x(A_3) + 1, y(A_3))]) → P_3
  26. GCD(a_2, d_2) → k_2
  27. Segment(A_3, P_3) → j_3
  28. Segment(D_2, S_2) → n_2
  29. Sequence(Sequence[CircleSector[(-1 * f * sin((2 * k - 1) * θ / 2) + 2.5 * (m - 1), f * cos((2 * k - 1) * θ / 2)), (-1 * f * sin((2 * k - 1) * θ / 2) - sin((k - 1) * θ) + 2.5 * (m - 1), f * cos((2 * k - 1) * θ / 2) + cos((k - 1) * θ)), (-1 * f * sin((2 * k - 1) * θ / 2) - sin(k * θ) + 2.5 * (m - 1), f * cos((2 * k - 1) * θ / 2) + cos(k * θ))], k, 1, 1], m, 1, a) → list4
  30. Sequence(Sequence[CircleSector[(f * sin((2 * k - 1) * θ / 2) + 2.5 * (m - 1), f * cos((2 * k - 1) * θ / 2)), (f * sin((2 * k - 1) * θ / 2) + sin(k * θ) + 2.5 * (m - 1), f * cos((2 * k - 1) * θ / 2) + cos(k * θ)), (f * sin((2 * k - 1) * θ / 2) + sin((k - 1) * θ) + 2.5 * (m - 1), f * cos((2 * k - 1) * θ / 2) + cos((k - 1) * θ))], k, 1, b], m, 1, a) → list3