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指数除法法则演示 by rmchugh1 (2)

指数除法法则演示 by rmchugh1 (2)
几何画板及绘图内容加载中，请稍等……
2013-09-10 09:53
解析几何
所属专题 Basic Exponents Rules Exponents Exponents Exponents Algebra: Exponents
①本范例演示指数除法法则在带有系数的代数表达式中的应用；②涉及核心数学概念包括指数运算规则、分数表示、几何变换；③构造要点使用了Text, If, Sequence, Translate, Polygon, FractionText, Segment等GeoGebra命令和对象，用于创建文本、条件判断、序列、平移、多边形、分数文本和线段；④适合高中数学教学，帮助学生理解和应用指数除法法则。

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. If(color, 255.0, 0.0) → factorColor255
  9. If(color, 153.0, 0.0) → factorColor153
  10. Text("x") → text3
  11. If(expX1 - expX2 ≟ 0.0 ∧ expY1 - expY2 ≟ 0.0, 1.0, 0.0) → zeros
  12. Sequence(Translate[xtop, Vector[(0.0, 0.0), (-(0.75) * i, 0.0)]], i, 0.0, expX1 - 1.0) → ExpandXtop
  13. Sequence(Translate[ytop, Vector[(0.0, 0.0), (0.75 * i, 0.0)]], i, 0.0, expY1 - 1.0) → ExpandYtop
  14. Sequence(Translate[xtop, Vector[(0.0, 0.0), (-(0.75) * i, -(1.2))]], i, 0.0, expX2 - 1.0) → ExpandXbot
  15. Sequence(Translate[ytop, Vector[(0.0, 0.0), (0.75 * i, -(1.2))]], i, 0.0, expY2 - 1.0) → ExpandYbot
  16. Translate((6.923609046978582, -1.782455570499752), Vector[Vector[(0.0, 0.0), (0.0, -3.0)]]) → A
  17. Translate((6.923609046978582, 0.217544429500248), Vector[Vector[(0.0, 0.0), (0.0, -3.0)]]) → B
  18. Translate((7.524258469913336, 0.217544429500248), Vector[Vector[(0.0, 0.0), (0.0, -3.0)]]) → C
  19. Translate((7.524258469913336, -1.782455570499752), Vector[Vector[(0.0, 0.0), (0.0, -3.0)]]) → D
  20. Polygon(A, B, C, D) → ShadeNotePoly, a_1, b_1, c_1, d_1
  21. 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
  22. 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
  23. Text("_________________________") → text7
  24. If(coef1 ≟ 0.0, 1.0, coef1) → coef1b
  25. FractionText(coef1b / coef2) → DivRuleFracText2
  26. FractionText(coef1b / coef2) → DivRuleFracText
  27. Segment(E, F) → a
  28. FractionText(coef1b / coef2) → ExpFormCoefOnlyText
  29. If(coef2 ≟ 0.0, 1.0, coef2) → coef2b
  30. Segment((7.5 - 0.75 * If[expX1 > expX2, expX1, expX2] - If[coef1b > 1.0 ∧ coef1b < 2.0 ∧ coef2b > 1.0 ∧ coef2b < 2.0, 0.0, If[coef1b < -(9.0) ∨ coef2b < -(9.0), 1.2, 0.7]], -(0.5)), (7.5 + 0.75 * If[expY1 > expY2, expY1, expY2], -(0.5))) → ExpandDivLine
  31. If(coef2 ≟ 0.0, Text[coef1b + ""], FractionText[coef1b / coef2b]) → ExpFrmCoefFraction
  32. Text(abs(expX1 - expX2) + "") → ExpandFracXexp
  33. Text(abs(expY1 - expY2) + "") → ExpandFracYexp
  34. FractionText(coef1b / coef2) → text13

AI 绘图提示语参考

画一个数学图形来演示指数除法规则，包含系数。图形中心是一个矩形，标注了变量 y 和 x 的轴。矩形上方和下方通过箭头指示指数变化，箭头数量与指数值相关。矩形内部显示系数相除的结果，以分数和小数两种形式表示。图形左侧和右侧有两组矩形，通过箭头连接，展示指数相减的过程。底部有一条线段，长度与指数差相关，并标注了系数相除的结果。
以上提示语为根据原始绘图命令整理而来，仅供参考。