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同分母分数加法 by Anthony OR 柯志明

同分母分数加法 by Anthony OR 柯志明
几何画板及绘图内容加载中，请稍等……
2018-04-29 09:51
多边形向量几何作图滑块动画函数图像
①本范例演示了同分母分数加法的几何表示，通过图形直观展示分数相加的过程；②涉及核心数学概念包括分数加法、几何图形表示、向量运算；③构造要点使用了Point, Translate, Vector, Polygon, Sequence, Segment, If等GeoGebra命令和对象，用于创建和操作图形元素；④适合初中数学教学，帮助学生理解分数加法的几何意义，提升空间想象能力。

GeoGebra 命令及参数

  1. Point(yAxis) → C
  2. Point(yAxis) → B
  3. Translate(B, Vector[(t2 * Vector[B, D])]) → B'
  4. Vector((0, 0), (-2.2, 0)) → u
  5. Point(yAxis) → A
  6. Polygon({A, A + (2, 0), A + (2, 1), A + (0, 1)}) → q1
  7. Polygon({B, B + (2, 0), B + (2, 1), B + (0, 1)}) → q2
  8. Sequence(Translate[q1, Vector[(i * u)]], i, 1, m) → L_1
  9. Sequence(Translate[q2, Vector[(i * u)]], i, 1, n) → L_2
  10. Polygon({A, A + ((2 * b / a), 0), A + ((2 * b / a), 1), A + (0, 1)}) → q3
  11. Sequence(Translate[q1, Vector[(i * u)]], i, 1, m) → L_5
  12. Polygon({B, B + ((2 * c / a), 0), B + ((2 * c / a), 1), B + (0, 1)}) → q4
  13. Sequence(Translate[q2, Vector[(i * u)]], i, 1, n) → L_6
  14. Sequence(Segment[A + ((i * 2 / a), 0), A + ((i * 2 / a), 1)], i, 1, a - 1) → L_3
  15. Sequence(Segment[B + ((i * 2 / a), 0), B + ((i * 2 / a), 1)], i, 1, a - 1) → L_4
  16. Polygon({C, C + (2, 0), C + (2, 1), C + (0, 1)}) → q5
  17. Translate(q3, Vector[(t1 * Vector[A, C])]) → q3'
  18. Translate(A, Vector[(t1 * Vector[A, C])]) → A'
  19. Sequence(Segment[A' + ((i * 2 / a), 0), A' + ((i * 2 / a), 1)], i, 0, b) → L_7
  20. Translate(q5, Vector[(-u)]) → q5'
  21. Sequence(Segment[A' + (0, i), A' + ((2 * b / a), i)], i, 0, 1) → L_9
  22. Polygon({B'', B'' + ((If[b + c > a, b + c - a, 0] * 2 / a), 0), B'' + ((If[b + c > a, b + c - a, 0] * 2 / a), 1), B'' + (0, 1)}) → q9
  23. Polygon({B', B' + ((If[b + c > a, a - b, c] * 2 / a), 0), B' + ((If[b + c > a, a - b, c] * 2 / a), 1), B' + (0, 1)}) → q8
  24. Sequence(Segment[B'' + ((i * 2 / a), 0), B'' + ((i * 2 / a), 1)], i, 0, If[b + c > a, b + c - a, 0]) → L_{11}
  25. Sequence(Segment[B' + (0, i), B' + ((If[b + c > a, a - b, c] * 2 / a), i)], i, 0, 1) → L_{12}
  26. Sequence(Segment[B'' + (0, i), B'' + ((If[b + c > a, b + c - a, 0] * 2 / a), i)], i, 0, 1) → L_{13}
  27. Translate(L_5, Vector[(t4 * Vector[A, C])]) → L_{14}
  28. Translate(L_1, Vector[(t4 * Vector[A, C])]) → L_{15}
  29. Translate(C, Vector[(m * u)]) → C'
  30. Translate(L_6, Vector[(t5 * Vector[B, C'])]) → L_{16}
  31. Translate(L_2, Vector[(t5 * Vector[B, C'])]) → L_{17}
  32. Sequence(Segment[B' + ((i * 2 / a), 0), B' + ((i * 2 / a), 1)], i, 0, If[b + c > a, a - b, c]) → L_{10}
  33. Sequence(Segment[C + ((i * 2 / a), 0), C + ((i * 2 / a), 1)], i, 1, a - 1) → L_{18}
  34. Sequence(Segment[E + ((i * 2 / a), 0), E + ((i * 2 / a), 1)], i, 1, a - 1) → L_8
  35. Segment(H, I) → f
  36. If(b > 0, 1, 0) → s1
  37. If(c > 0, 1, 0) → s2
  38. If(b + c > a, 1, 0) → s3
  39. If(m > 0, 1, 0) → s4
  40. If(n > 0, 1, 0) → s5
  41. If(s1 + s2 + s3 + s4 + s5 ≤ t1 + t2 + t3 + t4 + t5, true, false) → finished