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探索除法可视化

探索除法可视化
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2016-08-17 23:43
函数解析几何微积分参数方程几何作图
所属专题 CBSE Class VI Maths Multiplication and Division - Visuals Multiplication and Division - Visuals Multiplication and Division - Visuals
①本范例通过动态图形演示整数的除法运算及其余数的几何表示；②涉及核心数学概念包括除法、对数函数、不定积分、指数函数、多项式函数和参数方程；③构造要点运用了Textfield, If, Sequence, First, Last, Min, Max, Segment, Text等GeoGebra命令和对象，如n, divisor, dividendCircles等，实现动态交互和可视化；④适合高中及以上数学学习者，用于理解除法运算的几何意义和参数方程的应用。

GeoGebra 命令及参数

  1. Textfield(nText) → InputBox1
  2. If(n / divisor ≟ floor(n / divisor), false, true) → hasR
  3. Sequence(((-columns)) / 2 + i - 1 / 2, i, 1, columns) → xValues
  4. Sequence(((-divisor) - 1) / 2 + i, i, 1, divisor) → yValues
  5. First(Flatten[Sequence[Sequence[Point[{xValues(i), yValues(j)}], j, 1, Length[yValues]], i, 1, columns]], n) → list2
  6. If(hasR, First[list2, (divisor * Div[n, divisor])], list2) → dividendList
  7. Last(list2, n - (divisor * Div[n, divisor])) → remainderList
  8. Min(xValues) → left
  9. Max(xValues) → right
  10. Min(yValues) → bottom
  11. Max(yValues) → top
  12. Sequence(Circle[Element[dividendList, i], 0.4], i, 1, Length[dividendList]) → dividendCircles
  13. Sequence(Circle[Element[remainderList, i], 0.4], i, 1, Length[remainderList]) → remainderCircles
  14. Segment((left, bottom) + (-1 / 2, -1 / 2), (right, bottom) + (1 / 2, -1 / 2)) → i
  15. Segment((left, top) + (-1 / 2, 1 / 2), (right, top) + (1 / 2, 1 / 2)) → j
  16. Sequence(Segment[(left + i, bottom) + (-1 / 2, -1 / 2), (left + i, top) + (-1 / 2, 1 / 2)], i, 0, Length[xValues]) → dividendBoxes
  17. Text(If[hasR, " + " + (Mod[n, divisor]), ""]) → text4
  18. Sequence(Circle[Element[moving, i], 0.4], i, 1, Length[moving]) → movingCircles