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分数除法 by Jean Wong

分数除法 by Jean Wong
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2016-12-01 06:18
函数解析几何几何作图
该范例演示了分数除法的概念，即 a ÷ b = a/b。通过几何图形展示了部分除法的含义。涉及的核心数学概念包括分数和除法。使用了 Point, Segment, Sequence, Polygon, GCD 等 GeoGebra 命令进行构造。适合小学高年级或初中学生学习分数除法。

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 - 0.005, 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((0.016528925619834656, -3), (1.2165289256198346, -3), (1.2165289256198346, -1.3), (0.016528925619834656, -1.3)) → 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