积极 AI Logo 积极 AI

指数除法法则演示

指数除法法则演示
几何画板及绘图内容加载中，请稍等……
2017-11-21 22:29
函数微积分几何作图滑块动画
①本范例通过动态图形演示指数除法法则的应用，直观展示底数相同时指数相减的过程；②核心数学概念包括指数运算、函数图像变换、解析几何；③作图要点运用了Text, If, Sequence, Segment, Translate, Polygon等GeoGebra命令及对象，如expX1, expY1等，实现分步演示和交互式验证；④适合高中数学教学，用于帮助学生理解和掌握指数法则，增强数学可视化能力。

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) → factorColor255
  10. If(color, 153, 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 ∧ expY1 - expY2 ≟ 0, 1, 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), (((-0.75) * i), 0)]], i, 0, expX1 - 1) → ExpandXtop
  23. Sequence(Translate[ytop, Vector[(0, 0), ((0.75 * i), 0)]], i, 0, expY1 - 1) → ExpandYtop
  24. Sequence(Translate[xtop, Vector[(0, 0), (((-0.75) * i), (-1.2))]], i, 0, expX2 - 1) → ExpandXbot
  25. Sequence(Translate[ytop, Vector[(0, 0), ((0.75 * i), (-1.2))]], i, 0, expY2 - 1) → 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[(0, 0), (0, -3)]) → A
  28. Translate((6.923609046978582, 0.217544429500248), Vector[(0, 0), (0, -3)]) → B
  29. Translate((7.524258469913336, 0.217544429500248), Vector[(0, 0), (0, -3)]) → C
  30. Translate((7.524258469913336, -1.782455570499752), Vector[(0, 0), (0, -3)]) → 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), (((-0.73) * i), 0)]], Translate[(6.923609046978582, 0.4), Vector[(0, 0), (((-0.73) * i), 0)]], Translate[(7.524258469913336, 0.4), Vector[(0, 0), (((-0.73) * i), 0)]], Translate[(7.524258469913336, -1.782455570499752), Vector[(0, 0), (((-0.73) * i), 0)]]], i, 0, If[expX1 > expX2, expX2, expX1] - 1) → ExpandXPairsSeq
  33. Sequence(Polygon[Translate[(6.923609046978582, -1.782455570499752), Vector[(0, 0), ((0.73 * i), 0)]], Translate[(6.923609046978582, 0.4), Vector[(0, 0), ((0.73 * i), 0)]], Translate[(7.524258469913336, 0.4), Vector[(0, 0), ((0.73 * i), 0)]], Translate[(7.524258469913336, -1.782455570499752), Vector[(0, 0), ((0.73 * i), 0)]]], i, 1, If[expY1 > expY2, expY2, expY1]) → ExpandYPairsSeq

AI 绘图提示语参考

绘制一个动态演示指数除法规则的图形，展示相同底数时指数相减的过程。包含函数图像、滑动条控制变量，用文本标注指数值和运算过程，通过分段和向量可视化指数变化，并用多边形和分段线辅助解释。先画出基本框架，再根据滑动条数值动态生成指数变化的可视化部分，最后用多边形和分段线强调运算结果。
以上提示语为根据原始绘图命令整理而来，仅供参考。