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数列的表示

数列的表示
几何画板及绘图内容加载中，请稍等……
2019-03-13 01:24
函数数列微积分
本范例演示数列的不同表示方法。涉及的核心数学概念包括数列和级数。通过使用GeoGebra命令如Sequence、Flatten、Shuffle等，可以构造数列的递推公式、通项公式以及散点图。适合高中数学教学和学习。

GeoGebra 命令及参数

  1. Sequence(Polygon[{tableAnchor + (col1Width + col2Width + col3Width, 0 - (rowHeight * i)), tableAnchor + (col1Width + col2Width + col3Width + col4Width, 0 - (rowHeight * i)), tableAnchor + (col1Width + col2Width + col3Width + col4Width, 0 - (rowHeight * i) - rowHeight), tableAnchor + (col1Width + col2Width + col3Width, ((-rowHeight) * i) - rowHeight)}], i, 0, lastRow - 1) → tableCol4
  2. Sequence(Polygon[{tableAnchor + (col1Width + col2Width, 0 - (rowHeight * i)), tableAnchor + (col1Width + col2Width + col3Width, 0 - (rowHeight * i)), tableAnchor + (col1Width + col2Width + col3Width, 0 - (rowHeight * i) - rowHeight), tableAnchor + (col1Width + col2Width, ((-rowHeight) * i) - rowHeight)}], i, 0, lastRow - 1) → tableCol3
  3. Sequence(Polygon[{tableAnchor + (col1Width, 0 - (rowHeight * i)), tableAnchor + (col1Width + col2Width, 0 - (rowHeight * i)), tableAnchor + (col1Width + col2Width, 0 - (rowHeight * i) - rowHeight), tableAnchor + (col1Width, ((-rowHeight) * i) - rowHeight)}], i, 0, lastRow - 1) → tableCol2
  4. Flatten(Sequence[Sequence[(i, j), i, -8, -8 + (2 * (tileWidth + 1)), tileWidth + 1], j, 3, 3 - (2 * (tileHeight + 1)), (-tileHeight) - 1]) → fixedFrameAnchors
  5. Shuffle(fixedFrameAnchors) → shuffledFrameAnchors
  6. LaTeX(UnicodeToLetter[10003]) → cmark
  7. LaTeX(UnicodeToLetter[10007]) → xmark
  8. Sequence(Polygon[{tableAnchor + (0, 0 - (rowHeight * i)), tableAnchor + (col1Width, 0 - (rowHeight * i)), tableAnchor + (col1Width, 0 - (rowHeight * i) - rowHeight), tableAnchor + (0, ((-rowHeight) * i) - rowHeight)}], i, 0, lastRow - 1) → tableCol1
  9. LaTeX((((("\text{" * QUESTION) * "\\") * INSTRUCTIONS) * "}")) → TEXT
  10. Text("Recursion Formula", tableAnchor + (0.5 + col1Width, ((-rowHeight)) / 2)) → col2Header
  11. Text("General Term", tableAnchor + (0.5 + col1Width + col2Width, ((-rowHeight)) / 2)) → col3Header
  12. Text("Discrete Function", tableAnchor + (0.5 + col1Width + col2Width + col3Width, ((-rowHeight)) / 2)) → col4Header
  13. Text("160, 156, 152, \ldots", tableAnchor + (0, (-rowHeight) - rowHeight / 3), true, true) → sequence1
  14. Text("160, 80, \tfrac{160}{3}, \ldots", tableAnchor + (0, ((-rowHeight) * 3) - rowHeight / 3), true, true) → sequence3
  15. Text("160, 152, 140, \ldots", tableAnchor + (0, ((-rowHeight) * 2) - rowHeight / 3), true, true) → sequence2
  16. Zip(Polygon[A, A + (tileWidth, 0), A + (tileWidth, (-tileHeight)), A + (0, (-tileHeight))], A, shuffledFrameAnchors) → frames
  17. Element(frames, 1) → frame1
  18. Element(frames, 2) → frame2
  19. Element(frames, 3) → frame3
  20. Element(frames, 4) → frame4
  21. Element(frames, 5) → frame5
  22. Element(frames, 6) → frame6
  23. Element(frames, 7) → frame7
  24. Element(frames, 8) → frame8
  25. Element(frames, 9) → frame9
  26. Element(cells, 1) → cell1
  27. Element(frames, activeTile) → highlightedTile
  28. Element(cells, 2) → cell2
  29. Element(cells, 3) → cell3
  30. Element(cells, 4) → cell4
  31. Element(cells, 5) → cell5
  32. Element(cells, 7) → cell7
  33. Element(cells, 8) → cell8
  34. Element(cells, 9) → cell9
  35. Element(cells, activeCell) → highlightedCell
  36. Element(tableCol1, 1) → col1HeaderCell
  37. Text("Sequence", tableAnchor + (0.5, ((-rowHeight)) / 2)) → col1Header
  38. Element(tableCol2, 1) → col2HeaderCell
  39. Element(tableCol3, 1) → col3HeaderCell
  40. Element(tableCol4, 1) → col4HeaderCell
  41. Element(cells, 6) → cell6
  42. Zip(A ≟ B, A, itemsInCells, B, 1…9) → cellsCorrect
  43. Zip(Text[If[A, cmark, ""], Vertex[B, 2] + symbolOffset], A, cellsCorrect, B, cells) → cmarkList
  44. Zip(Text[If[¬A, xmark, ""], Vertex[B, 2] + symbolOffset], A, cellsCorrect, B, cells) → xmarkList
  45. LaTeX("\text{You found three different algebraic representations for each sequence.}") → feedback

AI 绘图提示语参考

绘制一个序列的多种表示形式，包括递推公式、通项公式和离散函数。首先画出一个表格，包含四列：递推公式、通项公式、离散函数和序列。然后在表格中输入三个序列：160, 156, 152, ...；160, 80, 160/3, ...；160, 152, 140, ...。接着在表格下方绘制九个方块，表示序列的项，并用不同颜色标记当前项。最后在表格上方添加标题：递推公式、通项公式、离散函数和序列。
以上提示语为根据原始绘图命令整理而来，仅供参考。