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立方体演示

立方体演示
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2018-12-19 07:45
数列解析几何立体几何微积分
①本范例演示立方体的构造与多面体特性；②涉及核心数学概念包括立体几何、数列、解析几何；③构造中运用了 Sequence（数列）、Sort（排序）、Remove（移除）等 GeoGebra 命令及对象如 n、originPoints、keepTheseCubes；④适合高中及以上学生用于理解三维图形与微积分中的上和下和（Riemann Sum）；

GeoGebra 命令及参数

  1. Sequence(Sequence[Sequence[Point[{i, j, k}], i, ((-n)) / 2, n / 2 - 1], j, ((-n)) / 2, n / 2 - 1], k, ((-n)) / 2, n / 2 - 1) → originPoints
  2. Sort(Flatten[Join[{{{Sequence[{(n * i) + 1, (n * (i + 1))}, i, 1, n - 2], Sequence[n^(3) + 1 - {(n * i) + 1, (n * (i + 1))}, i, 1, n - 2]}, Sequence[Sequence[i, i, Element[threeFaces, k] + 1, Element[threeFaces, k + 1] - 1], k, 1, Length[threeFaces], 2]}, Sequence[{(i * n^(2)) + 1, (i * n^(2)) + n, ((i + 1) * n^(2)) - n + 1, ((i + 1) * n^(2))}, i, 1, n - 2]}]]) → twoFaces
  3. Sort(Flatten[Sequence[Sequence[Sequence[{(k * n^(2)) + (i * n) + j}, k, 1, n - 2], i, 1, n - 2], j, 2, n - 1]]) → noFaces
  4. Remove(Sequence[i, i, 1, n^(3)], Flatten[Join[{noFaces, twoFaces, threeFaces}]]) → oneFace
  5. Element({noFaces, oneFace, twoFaces, threeFaces, Sequence[i, i, 1, n^(3)]}, i + 1) → keepTheseCubes
  6. Element({{}, KeepIf[x ≤ n^(2), oneFace], KeepIf[x ≤ n^(2), twoFaces], KeepIf[x ≤ n^(2), threeFaces], Sequence[i, i, 1, n^(2)]}, i + 1) → keepTheseColors
  7. RemoveUndefined(Flatten[Sequence[Sequence[Element[spacedPoints, i + j], i, 1, n], j, 0, Length[spacedPoints], n^(2)]]) → frontPoints
  8. Sequence(Element[Sequence[Polygon[Element[backPoints, i], Element[backPoints, i] + (1, 0, 0), Element[backPoints, i] + (1, 0, 1), Element[backPoints, i] + (0, 0, 1)], i, 1, Length[backPoints]], Element[keepTheseColors, j]], j, 1, Length[keepTheseColors]) → back
  9. Sequence(Element[spacedPoints, i], i, 1, n^(3), n) → leftPoints
  10. Flatten(First[spacedPoints, n^(2)]) → bottomPoints
  11. Sequence(Element[Sequence[Polygon[Element[frontPoints, i], Element[frontPoints, i] + (1, 0, 0), Element[frontPoints, i] + (1, 0, 1), Element[frontPoints, i] + (0, 0, 1)], i, 1, Length[frontPoints]], Element[keepTheseColors, j]], j, 1, Length[keepTheseColors]) → front
  12. Sequence(Element[Sequence[Polygon[Element[rightPoints, i], Element[rightPoints, i] + (0, 1, 0), Element[rightPoints, i] + (0, 1, 1), Element[rightPoints, i] + (0, 0, 1)], i, 1, Length[rightPoints]], Element[keepTheseColors, j]], j, 1, Length[keepTheseColors]) → right
  13. Sequence(Element[Sequence[Polygon[Element[topPoints, i], Element[topPoints, i] + (1, 0, 0), Element[topPoints, i] + (1, 1, 0), Element[topPoints, i] + (0, 1, 0)], i, 1, Length[topPoints]], Element[keepTheseColors, j]], j, 1, Length[keepTheseColors]) → top
  14. Sequence(Element[Sequence[Polygon[Element[bottomPoints, i], Element[bottomPoints, i] + (1, 0, 0), Element[bottomPoints, i] + (1, 1, 0), Element[bottomPoints, i] + (0, 1, 0)], i, 1, Length[bottomPoints]], Element[keepTheseColors, j]], j, 1, Length[keepTheseColors]) → bottom
  15. Sequence(Element[Sequence[Polygon[Element[leftPoints, i], Element[leftPoints, i] + (0, 1, 0), Element[leftPoints, i] + (0, 1, 1), Element[leftPoints, i] + (0, 0, 1)], i, 1, Length[leftPoints]], Element[keepTheseColors, j]], j, 1, Length[keepTheseColors]) → left
  16. Sequence(Element[Sequence[Cube[Element[spacedPoints, i], Element[spacedPoints, i] + (1, 0, 0), Element[spacedPoints, i] + (1, 1, 0)], i, 1, Length[spacedPoints]], Element[keepTheseCubes, j]], j, 1, Length[keepTheseCubes]) → allSmallCubes

AI 绘图提示语参考

绘制一个立方体演示图，展示立方体的构造和性质。首先生成一个立方体网格，包含所有顶点。然后，根据顶点位置和可见性，绘制立方体的各个面，区分单面、双面、三面和全可见的面。使用不同颜色标记这些面，并确保每个立方体的小面都正确显示。最后，将所有小立方体组合起来，形成一个完整的立方体集合，以展示立体几何和序列的数学概念。
以上提示语为根据原始绘图命令整理而来，仅供参考。