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分数除法演示 by Mr Tsang

分数除法演示 by Mr Tsang
几何画板及绘图内容加载中，请稍等……
2018-04-08 21:00
函数极限几何作图滑块动画
①本范例通过动态演示分数除法的几何意义，直观展示分数除法与乘法的互逆关系；②涉及核心数学概念包括分数运算、除法性质、几何直观；③构造要点：使用 Point, Segment, Sequence, Polygon, GCD, Text 等命令创建分数表示的图形，通过 l1, l2, l3 等对象展示运算过程；④适合初中及以上数学教学，用于理解分数除法的本质和几何应用。

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(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) → list4
  10. Sequence(Segment[((2.5 * a), 0), ((2.5 * a) - sin((j * θ)), cos((j * θ)))], j, 1, c - 1) → list2
  11. Segment(D, (x(D) + 1, y(D))) → l4
  12. Polygon(E, (x(E) + 1, y(E)), E + (1, 1.6), E + (0, 1.6)) → poly1, g, h, i, p
  13. GCD(a, d) → k
  14. Segment(A, P) → j
  15. Segment(C, R) → l
  16. Segment(B, Q) → m
  17. Segment(D, S) → n
  18. 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 - 1) * θ)) + (2.5 * (m - 1)), (f * cos((((2 * k) - 1) * θ / 2))) + cos(((k - 1) * θ))), (((-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) → list6
  19. Text(a + (" cake" * If[a > 1, "s are ", " is "]) + ((("shared equally among " * b) * " students. How many cakes will each student get?"))) → text6
  20. Text(If[e, "Expression", "算式"]) → text11
  21. Text(a + "個蛋糕，讓" + b + "位學生均分。每位學生分得多少個蛋糕？") → text12