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分数作为正方形的部分

分数作为正方形的部分
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2014-02-18 21:58
多边形解析几何
①这个范例演示了如何用正方形分割来直观理解分数的概念；②涉及的核心数学概念包括分数、正方形、极限、逻辑和组合数学；③作图要点使用了GeoGebra的If和Sequence命令，创建了多个对象如A1-A10、C1-C10等来表示分割的部分和计算质心；④适合初中及以上学生学习分数、几何分割和质心计算，也可用于数学教学演示。

GeoGebra 命令及参数

  1. If(a - ((A1 - 1) * b) > 0, If[a - ((A1 - 1) * b) < b, a - ((A1 - 1) * b), b], 0) → B1
  2. If(a - ((A2 - 1) * b) > 0, If[a - ((A2 - 1) * b) < b, a - ((A2 - 1) * b), b], 0) → B2
  3. If(a - ((A3 - 1) * b) > 0, If[a - ((A3 - 1) * b) < b, a - ((A3 - 1) * b), b], 0) → B3
  4. If(a - ((A4 - 1) * b) > 0, If[a - ((A4 - 1) * b) < b, a - ((A4 - 1) * b), b], 0) → B4
  5. If(a - ((A5 - 1) * b) > 0, If[a - ((A5 - 1) * b) < b, a - ((A5 - 1) * b), b], 0) → B5
  6. If(a - ((A6 - 1) * b) > 0, If[a - ((A6 - 1) * b) < b, a - ((A6 - 1) * b), b], 0) → B6
  7. If(a - ((A7 - 1) * b) > 0, If[a - ((A7 - 1) * b) < b, a - ((A7 - 1) * b), b], 0) → B7
  8. If(a - ((A8 - 1) * b) > 0, If[a - ((A8 - 1) * b) < b, a - ((A8 - 1) * b), b], 0) → B8
  9. If(a - ((A9 - 1) * b) > 0, If[a - ((A9 - 1) * b) < b, a - ((A9 - 1) * b), b], 0) → B9
  10. If(a - ((A10 - 1) * b) > 0, If[a - ((A10 - 1) * b) < b, a - ((A10 - 1) * b), b], 0) → B10
  11. Sequence(Polygon[C1 + ((0, 1 / b) * i), D1 + ((0, 1 / b) * i), D1 + ((0, 1 / b) * (i + 1)), C1 + ((0, 1 / b) * (i + 1))], i, 0, B1 - 1) → E1
  12. Sequence(Polygon[C3 + ((0, 1 / b) * i), D3 + ((0, 1 / b) * i), D3 + ((0, 1 / b) * (i + 1)), C3 + ((0, 1 / b) * (i + 1))], i, 0, B3 - 1) → E3
  13. Sequence(Polygon[C5 + ((0, 1 / b) * i), D5 + ((0, 1 / b) * i), D5 + ((0, 1 / b) * (i + 1)), C5 + ((0, 1 / b) * (i + 1))], i, 0, B5 - 1) → E5
  14. Sequence(Polygon[C7 + ((0, 1 / b) * i), D7 + ((0, 1 / b) * i), D7 + ((0, 1 / b) * (i + 1)), C7 + ((0, 1 / b) * (i + 1))], i, 0, B7 - 1) → E7
  15. Sequence(Polygon[C9 + ((0, 1 / b) * i), D9 + ((0, 1 / b) * i), D9 + ((0, 1 / b) * (i + 1)), C9 + ((0, 1 / b) * (i + 1))], i, 0, B9 - 1) → E9
  16. Sequence(Polygon[C7 + ((1 / b, 0) * i), D1 + ((1 / b, 0) * i), D1 + ((1 / b, 0) * (i + 1)), C7 + ((1 / b, 0) * (i + 1))], i, 0, B2 - 1) → E2
  17. Sequence(Polygon[C9 + ((1 / b, 0) * i), D3 + ((1 / b, 0) * i), D3 + ((1 / b, 0) * (i + 1)), C9 + ((1 / b, 0) * (i + 1))], i, 0, B4 - 1) → E4
  18. Sequence(Polygon[C6 + (0, 1) + ((1 / b, 0) * i), C6 + ((1 / b, 0) * i), C6 + ((1 / b, 0) * (i + 1)), C6 + (0, 1) + ((1 / b, 0) * (i + 1))], i, 0, B6 - 1) → E6
  19. Sequence(Polygon[C8 + (0, 1) + ((1 / b, 0) * i), C8 + ((1 / b, 0) * i), C8 + ((1 / b, 0) * (i + 1)), C8 + (0, 1) + ((1 / b, 0) * (i + 1))], i, 0, B8 - 1) → E8
  20. Sequence(Polygon[C10 + (0, 1) + ((1 / b, 0) * i), C10 + ((1 / b, 0) * i), C10 + ((1 / b, 0) * (i + 1)), C10 + (0, 1) + ((1 / b, 0) * (i + 1))], i, 0, B10 - 1) → E10
  21. Sequence(Polygon[Cell[3, i], Cell[4, i], Cell[4, i + 5], Cell[3, i + 5]], i, 1, 5) → squares1
  22. Sequence(Polygon[Cell[3, i], Cell[4, i], Cell[4, i] + (0, 1), Cell[3, i] + (0, 1)], i, 6, 10) → squares2