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单位分数可视化：用矩形条与黎曼和探索分数分解

单位分数可视化：用矩形条与黎曼和探索分数分解
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2019-06-16 01:01
多边形数列积分滑块动画
① 本范例通过动态矩形条带和点阵图，直观展示单位分数（分子为1的分数）的几何表示与分解过程，帮助理解分数与面积、长度之间的关系。② 核心数学概念包括单位分数、分数比较、矩形面积模型、黎曼和（上和与下和）以及整数与中位数的应用，将分数运算与微积分初步思想联系起来。③ 作图要点：使用GeoGebra的Random、Element、Sequence命令生成随机分数和列表，通过Segment、Point、OrthogonalLine、Intersect构造矩形边界与垂直分割线，Polygon绘制分数条，并利用滑块（chooser、denominator）和按钮（showanswer、reset）控制交互显示答案与重置。④ 适合小学高年级至初中阶段学习分数概念，也可用于高中引入黎曼和与积分思想的直观铺垫，是数学课堂中兼具操作性与启发性的动态教具。

GeoGebra 命令及参数

  1. Random(5, 12) → lengthoftape
  2. Random(1, 6) → chooser
  3. Element(list2, chooser) → denominator
  4. Sequence((x(A) + (i * fractionwidth), y(A) + tapeheight), i, 0, denominator) → DotsTop
  5. Sequence((x(A) + (i * fractionwidth), y(A)), i, 0, denominator) → DotsBottom
  6. Sequence(Segment[Element[DotsBottom, i], Element[DotsTop, i]], i, 1, denominator + 1) → drawverticals
  7. Segment(Element[DotsBottom, 1], Element[DotsBottom, denominator + 1]) → horizontalbottom
  8. Segment(Element[DotsTop, 1], Element[DotsTop, denominator + 1]) → horizontaltop
  9. Segment(Element[DotsBottom, 1], Element[DotsTop, 1]) → verticalleft
  10. Segment(Element[DotsBottom, denominator + 1], Element[DotsTop, denominator + 1]) → verticalright
  11. Point(horizontalbottom) → B
  12. Point(horizontalbottom) → C
  13. OrthogonalLine(C, horizontalbottom) → f
  14. Point(horizontalbottom) → D
  15. Point(horizontalbottom) → E
  16. Point(horizontalbottom) → F
  17. Point(horizontalbottom) → G
  18. Point(horizontalbottom) → H
  19. Point(horizontalbottom) → I
  20. Point(horizontalbottom) → J
  21. Point(horizontalbottom) → K
  22. OrthogonalLine(B, horizontaltop) → g
  23. OrthogonalLine(D, horizontaltop) → h
  24. OrthogonalLine(E, horizontaltop) → i
  25. OrthogonalLine(F, horizontaltop) → j
  26. OrthogonalLine(G, horizontaltop) → k
  27. OrthogonalLine(H, horizontaltop) → l
  28. OrthogonalLine(I, horizontaltop) → m
  29. OrthogonalLine(J, horizontaltop) → n
  30. OrthogonalLine(K, horizontaltop) → p
  31. Intersect(f, horizontaltop) → L
  32. Intersect(g, horizontaltop) → M
  33. Intersect(h, horizontaltop) → N
  34. Intersect(i, horizontaltop) → O
  35. Intersect(j, horizontaltop) → P
  36. Intersect(k, horizontaltop) → Q
  37. Intersect(l, horizontaltop) → R
  38. Intersect(m, horizontaltop) → S
  39. Intersect(n, horizontaltop) → T
  40. Intersect(p, horizontaltop) → U
  41. Segment(C, L) → q
  42. Segment(B, M) → r
  43. Segment(D, N) → s
  44. Segment(E, O) → t
  45. Segment(F, P) → a
  46. Segment(G, Q) → b
  47. Segment(H, R) → c
  48. Segment(I, S) → d
  49. Segment(J, T) → e
  50. Segment(K, U) → f_1
  51. Sequence(Element[DotsTop, i], i, 2, denominator) → DotsTopRevealed
  52. Polygon(Element[DotsBottom, 1], Element[DotsBottom, denominator + 1], Element[DotsTop, denominator + 1], Element[DotsTop, 1]) → poly1, g_1, h_1, i_1, j_1