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指数除法法则演示 by rmchugh1

指数除法法则演示 by rmchugh1
几何画板及绘图内容加载中，请稍等……
2013-09-10 09:51
三角函数几何作图
所属专题 Basic Exponents Rules Exponents Exponents Exponents
①本范例演示指数除法法则的几何表示与计算过程；②涉及核心数学概念包括指数运算、分数化简、几何变换；③构造要点运用了Text, If, Sequence, Segment, Translate, Polygon等GeoGebra命令与对象，实现动态图形与文本说明；④适合高中数学教学与学习，帮助理解指数性质与几何直观。

GeoGebra 命令及参数

  1. Text("y") → text4
  2. Text("y") → text6
  3. Text("x") → text5
  4. Text(expX1 + "") → text8
  5. Text(expX2 + "") → text9
  6. Text(expY1 + "") → text10
  7. Text(expY2 + "") → text11
  8. Text("________________") → origFracLine
  9. If(color, 255.0, 0.0) → factorColor255
  10. If(color, 153.0, 0.0) → factorColor153
  11. Text("x") → text3
  12. Text("________________") → fracLine
  13. Text(abs(expX1 - expX2) + "") → fracXbotYbotExp
  14. Text(abs(expY1 - expY2) + "") → fracYbotXbotExp
  15. Text(expY1 - expY2 + "") → fracYtopXbotExp
  16. Text(abs(expX1 - expX2) + "") → fracXbotYtopExp
  17. If(expX1 - expX2 ≟ 0.0 ∧ expY1 - expY2 ≟ 0.0, 1.0, 0.0) → zeros
  18. Text(expX1 - expX2 + "") → fracXtopYtopExp
  19. Text(abs(expY1 - expY2) + "") → fracYbotXtopExp
  20. Text(expX1 - expX2 + "") → fracXtopYbotExp
  21. Text(expY1 - expY2 + "") → fracYtopXtopExp
  22. Sequence(Translate[xtop, Vector[(0.0, 0.0), (-(0.75) * i, 0.0)]], i, 0.0, expX1 - 1.0) → ExpandXtop
  23. Sequence(Translate[ytop, Vector[(0.0, 0.0), (0.75 * i, 0.0)]], i, 0.0, expY1 - 1.0) → ExpandYtop
  24. Sequence(Translate[xtop, Vector[(0.0, 0.0), (-(0.75) * i, -(1.2))]], i, 0.0, expX2 - 1.0) → ExpandXbot
  25. Sequence(Translate[ytop, Vector[(0.0, 0.0), (0.75 * i, -(1.2))]], i, 0.0, expY2 - 1.0) → ExpandYbot
  26. Segment((7.5 - 0.75 * If[expX1 > expX2, expX1, expX2], -(0.5)), (7.5 + 0.75 * If[expY1 > expY2, expY1, expY2], -(0.5))) → ExpandDivLine
  27. Translate((6.923609046978582, -1.782455570499752), Vector[Vector[(0.0, 0.0), (0.0, -3.0)]]) → A
  28. Translate((6.923609046978582, 0.217544429500248), Vector[Vector[(0.0, 0.0), (0.0, -3.0)]]) → B
  29. Translate((7.524258469913336, 0.217544429500248), Vector[Vector[(0.0, 0.0), (0.0, -3.0)]]) → C
  30. Translate((7.524258469913336, -1.782455570499752), Vector[Vector[(0.0, 0.0), (0.0, -3.0)]]) → D
  31. Polygon(A, B, C, D) → ShadeNotePoly, a_1, b_1, c_1, d_1
  32. Sequence(Polygon[Translate[(6.923609046978582, -1.782455570499752), Vector[(0.0, 0.0), (-(0.73) * i, 0.0)]], Translate[(6.923609046978582, 0.4), Vector[(0.0, 0.0), (-(0.73) * i, 0.0)]], Translate[(7.524258469913336, 0.4), Vector[(0.0, 0.0), (-(0.73) * i, 0.0)]], Translate[(7.524258469913336, -1.782455570499752), Vector[(0.0, 0.0), (-(0.73) * i, 0.0)]]], i, 0.0, If[expX1 > expX2, expX2, expX1] - 1.0) → ExpandXPairsSeq
  33. Sequence(Polygon[Translate[(6.923609046978582, -1.782455570499752), Vector[(0.0, 0.0), (0.73 * i, 0.0)]], Translate[(6.923609046978582, 0.4), Vector[(0.0, 0.0), (0.73 * i, 0.0)]], Translate[(7.524258469913336, 0.4), Vector[(0.0, 0.0), (0.73 * i, 0.0)]], Translate[(7.524258469913336, -1.782455570499752), Vector[(0.0, 0.0), (0.73 * i, 0.0)]]], i, 1.0, If[expY1 > expY2, expY2, expY1]) → ExpandYPairsSeq

AI 绘图提示语参考

绘制一个几何图形来演示指数除法规则，包含两个指数表达式，用分数形式表示它们的除法，并展示几何变换过程。首先画出两个指数表达式，标注它们的值，然后用分数线连接，接着通过几何变换（平移和缩放）来可视化指数除法的结果，最后用多边形和线条来强调几何意义。
以上提示语为根据原始绘图命令整理而来，仅供参考。