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特殊幂值

特殊幂值
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2024-10-02 20:26
解析几何几何作图
所属专题 Rechnen mit Potenzen
本范例通过多个选择题和开放题，演示了特殊幂值的计算方法。涉及的核心数学概念包括幂的运算规则。使用了 GeoGebra 的多种命令，如 Textfield, Sequence, Join 等。适合初中7-8年级学生学习幂的运算规则。

GeoGebra 命令及参数

  1. Textfield(input1) → InputBox1
  2. Textfield(input2) → InputBox2
  3. Textfield(input3) → InputBox3
  4. Textfield(input4) → InputBox4
  5. SpeechBubbleRight(A, 11, 1.8) → Speech1
  6. Sequence(B + ((dfx * i), 0), i, 0, size, 1) → Layer1Points
  7. Sequence(D + ((dfx * i), 0), i, 0, size, 1) → Layer3Points
  8. Sequence(C + ((dfx * i), 0), i, 0, size, 1) → Layer2Points
  9. Join({{Segment[C, Layer2Points(Length[Layer2Points])], Segment[B, Layer1Points(Length[Layer1Points])]}, Sequence[Segment[Layer1Points(i), Layer2Points(i)], i, 1, Length[Layer1Points], 1]}) → Kanten1
  10. Translate(Layer1Points, (Length[Vector[B, Layer1Points(2)] / 2], -0.2)) → BogenUntenStartEndList
  11. Translate(Layer1Points, (Length[Vector[B, Layer1Points(2)]], -0.2 - Length[Vector[B, Layer1Points(2)] / 2])) → BogenUntenMidList
  12. Join({{Segment[C, Layer2Points(Length[Layer2Points])], Segment[D, Layer3Points(Length[Layer3Points])]}, Sequence[Segment[Layer3Points(i), Layer2Points(i)], i, 1, Length[Layer1Points], 1]}) → Kanten2
  13. Textfield(input5) → InputBox5
  14. Textfield(inputText) → Eingabefeld1
  15. SpeechBubbleRight(A, 8.4, 1.8) → Speech2
  16. Translate(Layer3Points, (Length[Vector[B, Layer1Points(2)] / 2], 0.2)) → BogenObenStartEndList
  17. Translate(Layer3Points, (Length[Vector[B, Layer1Points(2)]], 0.2 + Length[Vector[B, Layer1Points(2)] / 2])) → BogenObenMidList
  18. Text(Div2Text, BogenObenMidList(4) + (0, 0.5), false, true, 0, 0) → Text12
  19. Text(Div2Text, BogenObenMidList(3) + (0, 0.5), false, true, 0, 0) → Text13
  20. Text(Div2Text, BogenObenMidList(1) + (0, 0.5), false, true, 0, 0) → Text15
  21. Text(Div2Text, BogenObenMidList(2) + (0, 0.5), false, true, 0, 0) → Text14
  22. Textfield(input6) → InputBox6
  23. Sequence(Text[Mult2Text, BogenUntenMidList(i) + (0, -0.25), false, true, 0, 0], i, 1, 4, 1) → Mult2Besch
  24. SpeechBubbleRight(A, 8.4, 1.8) → Vieleck1
  25. If(step < 8, 8 - step - 1, 0) → inputsol
  26. Sequence(CircumcircleArc[BogenUntenStartEndList(i), BogenUntenMidList(i) + (-0.3, 0), BogenUntenStartEndList(i + 1) + (-0.3, 0)], i, 1, 4, 1) → Mult2Bogen
  27. Sequence(BogenUntenStartEndList(i) + (-0.3, 0), i, 2, 5, 1) → Mult2Pfeile
  28. CircumcircleArc(BogenObenStartEndList(5), BogenObenMidList(4), BogenObenStartEndList(4) + (0.3, 0)) → BogenOben1
  29. CircumcircleArc(BogenObenStartEndList(4), BogenObenMidList(3), BogenObenStartEndList(3) + (0.3, 0)) → BogenOben2
  30. CircumcircleArc(BogenObenStartEndList(3), BogenObenMidList(2), BogenObenStartEndList(2) + (0.3, 0)) → BogenOben3
  31. CircumcircleArc(BogenObenStartEndList(2), BogenObenMidList(1), BogenObenStartEndList(1) + (0.3, 0)) → BogenOben4

AI 绘图提示语参考

在坐标平面上准备若干输入框用于选择题：在底部生成四条等间距的点列，分别以三条相邻点之间的弦连成折线边界，并在两层点列之间画出连续的相邻连接线；同时在顶部生成对应的另一层弧形点列，并用把相邻点按层两两连接形成上部折线边界。再把底部与顶部各两端之间做四段圆弧，圆弧的中点用点列的中间位置控制。最后在圆弧对应位置叠加4个小符号/数字提示，并在图中加入若干右侧气泡用于说明“每一段对应的幂/规则”。
以上提示语为根据原始绘图命令整理而来，仅供参考。