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除法决策

除法决策
几何画板及绘图内容加载中，请稍等……
2018-12-20 21:56
向量立体几何几何作图
①本范例演示了三维空间中除法与分数的几何表示，通过动态交互展示向量与体积关系；②涉及核心概念包括除法、分数、三维向量、几何分布、体积计算、减法及圆锥体积；③构造中运用了If, First, Numerator, Denominator, Flatten, Sequence, Zip, Textfield, Length等GeoGebra命令及对象，如n1Text, n2Text, n1, n2, n1n2num等；④适合高中及以上数学学习者，用于理解空间几何与代数运算的结合应用。

GeoGebra 命令及参数

  1. If(n2Text ≠ "" ∧ floor(FromBase[n2Text, 10]) ≟ FromBase[n2Text, 10], FromBase[n2Text, 10], 1) → n2
  2. If(n1Text ≠ "" ∧ floor(FromBase[n1Text, 10]) ≟ FromBase[n1Text, 10], FromBase[n1Text, 10], 1) → n1
  3. If(n2 > n1, 1, n1^(0.5) / n2^(0.5)) → n2ArraySpacer
  4. If(n1 > n2, 1, n2^(0.5) / n1^(0.5)) → n1ArraySpacer
  5. First(Flatten[Sequence[Sequence[Point[{(i * n2ArraySpacer), (j * n2ArraySpacer)}], j, ((-(ceil(n2^(0.5)) - 1))) / 2, (ceil(n2^(0.5)) - 1) / 2], i, 1, ceil(n2^(0.5))]], n2) → n2Anchors
  6. Numerator(n1divn2) → n1n2num
  7. Denominator(n1divn2) → n1n2den
  8. First(Flatten[Sequence[Sequence[Point[{((-i) * n1ArraySpacer), (j * n1ArraySpacer)}], j, ((-(ceil(n1^(0.5)) - 1))) / 2, (ceil(n1^(0.5)) - 1) / 2], i, 1, ceil(n1^(0.5))]], n1) → n1Anchors
  9. Flatten(Sequence[Sequence[Element[n1Anchors, i], j, 1, n1n2den], i, 1, n1]) → n1n2StartingPoints
  10. Sequence(Sequence[Element[n2Anchors, j] + ((((1 - (0.8 * ceil(n1 / n2)^(-0.5))) * n2OrigCircleSize) * cos((i * π / π))), (((1 - (0.8 * ceil(n1 / n2)^(-0.5))) * n2OrigCircleSize) * sin((i * π / π)))), i, 0, (2 * π) - 1 / ceil(n1 / n2), (2 * π / ceil(n1 / n2))], j, 1, n2) → n1n2TargetHelper
  11. If(n1 > n2, Join[{Sequence[n1n2den, i, 1, n1divn2], {n1n2num - (n1n2den * floor(n1divn2))}}], {n1}) → n1n2BreakdownHelper
  12. Zip(Circle[AAA, n1OrigCircleSize], AAA, n1Anchors) → n1Circles
  13. Zip(Circle[AAA, n2OrigCircleSize], AAA, n2Anchors) → n2Circles
  14. Flatten(Sequence[Sequence[i, j, 1, Element[n1n2BreakdownHelper, i]], i, 1, Length[n1n2BreakdownHelper]]) → n1n2Breakdown
  15. If(n1 > n2, Flatten[Sequence[Sequence[Element[n1n2TargetHelper, i, Element[n1n2Breakdown, j]], j, 1, Length[n1n2Breakdown]], i, 1, Length[n1n2TargetHelper]]], Flatten[Sequence[Sequence[Element[n2Anchors, i], j, 1, n1n2num], i, 1, n2]]) → n1n2EndingPoints
  16. Denominator(n1divn2) → n2n1num
  17. Numerator(n1divn2) → n2n1den
  18. If(n2 > n1, Join[{Sequence[n2n1den, i, 1, n2divn1], {n2n1num - (n2n1den * floor(n2divn1))}}], {n2}) → n2n1BreakdownHelper
  19. Flatten(Sequence[Sequence[i, j, 1, Element[n2n1BreakdownHelper, i]], i, 1, Length[n2n1BreakdownHelper]]) → n2n1Breakdown
  20. Flatten(Sequence[Sequence[Element[n2Anchors, i], j, 1, n2n1den], i, 1, n2]) → n2n1StartingPoints
  21. Sequence(Sequence[Element[n1Anchors, j] + ((((1 - (0.8 * ceil(n2 / n1)^(-0.5))) * n1OrigCircleSize) * cos((i * π / π))), (((1 - (0.8 * ceil(n2 / n1)^(-0.5))) * n1OrigCircleSize) * sin((i * π / π)))), i, 0, (2 * π) - 1 / ceil(n2 / n1), (2 * π / ceil(n2 / n1))], j, 1, n1) → n2n1TargetHelper
  22. Textfield(n1Text) → InputBox1
  23. Textfield(n2Text) → InputBox2
  24. If(n2 > n1, Flatten[Sequence[Sequence[Element[n2n1TargetHelper, i, Element[n2n1Breakdown, j]], j, 1, Length[n2n1Breakdown]], i, 1, Length[n2n1TargetHelper]]], Flatten[Sequence[Sequence[Element[n1Anchors, i], j, 1, n2n1num], i, 1, n1]]) → n2n1EndingPoints
  25. Zip((AAA * (2 - Max[(-a), 1])) + (BBB * Max[(-a) - 1, 0]), AAA, n2n1StartingPoints, BBB, n2n1EndingPoints) → n2n1MovingPoints
  26. Flatten(Sequence[Sector[Circle[Element[n2n1MovingPoints, i], n2n1CircleSize], ((2 * π / n2n1den) * Mod[i, n2n1den]), ((2 * π / n2n1den) * (Mod[i, n2n1den] + 1))], i, 1, Length[n2n1MovingPoints]]) → n2n1Wedges
  27. Zip((AAA * (2 - Max[a, 1])) + (BBB * Max[a - 1, 0]), AAA, n1n2StartingPoints, BBB, n1n2EndingPoints) → n1n2MovingPoints
  28. Flatten(Sequence[Sector[Circle[Element[n1n2MovingPoints, i], n1n2CircleSize], ((2 * π / n1n2den) * Mod[i, n1n2den]), ((2 * π / n1n2den) * (Mod[i, n1n2den] + 1))], i, 1, Length[n1n2MovingPoints]]) → n1n2Wedges
  29. Length(n2n1EndingPoints) → b
  30. Length(n2n1StartingPoints) → c

AI 绘图提示语参考

在三维空间中展示一个动态的几何图形，通过两个向量展示分数和除法的几何表示。图形包含两个不同大小的圆形，每个圆形上有多个点，这些点通过线段连接形成网格。根据输入的两个数值，图形会动态调整网格的大小和分布，展示分数的几何意义。网格中的点会根据分数的值移动，形成不同的形状，最终展示出分数和除法的几何关系。
以上提示语为根据原始绘图命令整理而来，仅供参考。