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等价表达式 GeoGebra 示例

等价表达式 GeoGebra 示例
几何画板及绘图内容加载中，请稍等……
2019-01-19 02:52
函数概率统计几何作图
①本范例通过 GeoGebra 动态演示等价表达式的数学概念；②涉及核心概念包括代数运算、条件概率、等腰三角形、平行四边形等；③构造要点运用了 Sequence, Join, LaTeX, Element, Zip, Text 等命令及 tileWidthShorter, tileHeight 等对象；④适合高中数学教学，用于理解代数变形与几何直观的结合。

GeoGebra 命令及参数

  1. Sequence((-8 + tileWidthLong + 1 + tileWidthShort + 1, j), j, 3, 3 - (3 * tileHeight), (-(1 + tileHeight))) → fixedFrames3
  2. Sequence((-8 + tileWidthLong + 1, j), j, 3, 3 - (3 * tileHeight), (-(1 + tileHeight))) → fixedFrames2
  3. Sequence((-8, j), j, 3, 3 - (3 * tileHeight), (-(1 + tileHeight))) → fixedFrames1
  4. 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
  5. Join({fixedFrames1, fixedFrames2, fixedFrames3}) → fixedFrameAnchors
  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. Join({Zip[Polygon[A, A + (tileWidthLong, 0), A + (tileWidthLong, (-tileHeight)), A + (0, (-tileHeight))], A, fixedFrames1], Zip[Polygon[A, A + (tileWidthShort, 0), A + (tileWidthShort, (-tileHeight)), A + (0, (-tileHeight))], A, fixedFrames2], Zip[Polygon[A, A + (tileWidthShorter, 0), A + (tileWidthShorter, (-tileHeight)), A + (0, (-tileHeight))], A, fixedFrames3]}) → frames
  11. Element(frames, 1) → frame1
  12. Element(frames, 2) → frame2
  13. Element(frames, 3) → frame3
  14. Element(frames, 4) → frame4
  15. Element(frames, 5) → frame5
  16. Element(frames, 6) → frame6
  17. Element(frames, 7) → frame7
  18. Element(frames, 8) → frame8
  19. Element(frames, 9) → frame9
  20. Element(cells, 1) → cell1
  21. Element(cells, 2) → cell2
  22. Element(cells, 3) → cell3
  23. Element(cells, 4) → cell4
  24. Element(cells, 5) → cell5
  25. Element(cells, activeCell) → highlightedCell
  26. Element(tableCol1, 1) → col1HeaderCell
  27. Element(tableCol2, 1) → col2HeaderCell
  28. Zip(A ≟ B, A, itemsInCells, B, {7, 2, 3, 6, 1}) → cellsCorrect
  29. Zip(Text[If[A, cmark, ""], Vertex[B, 2] + symbolOffset], A, cellsCorrect, B, cells) → cmarkList
  30. Zip(Text[If[¬A, xmark, ""], Vertex[B, 2] + symbolOffset], A, cellsCorrect, B, cells) → xmarkList
  31. Text("... is equivalent to this expression", tableAnchor + (0.25 + col1Width, ((-rowHeight)) / 1.75)) → col2Header
  32. Text("This expression ...", tableAnchor + (0.25, ((-rowHeight)) / 1.75)) → col1Header
  33. LaTeX("\text{You found the equivalent expressions.}") → feedback
  34. Element(frames, activeTile) → highlightedTile
  35. Text("(1-x)(x-3)^2", tableAnchor + (0.25, ((-rowHeight) * 5) - 0.3), true, true) → expression5
  36. Text("x^3+3x^2+3x+1", tableAnchor + (0.25, ((-rowHeight) * 4) - 0.3), true, true) → expression4
  37. Text("(x+y+3)^2", tableAnchor + (0.25, ((-rowHeight) * 3) - 0.3), true, true) → expression3
  38. Text("(x+3)(-3x-11)", tableAnchor + (0.25, ((-rowHeight) * 2) - 0.3), true, true) → expression2
  39. Text("x^2-16x+64", tableAnchor + (0.25, (-rowHeight) - 0.3), true, true) → expression1