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网格中的面积乐趣

网格中的面积乐趣
几何画板及绘图内容加载中，请稍等……
2023-05-25 03:14
多边形解析几何几何作图滑块动画
本范例通过在网格上使用单位正方形构建图形，探索矩形、正方形和组合图形的面积。①本范例演示如何在网格上构建图形并计算其面积；②涉及的核心数学概念包括面积计算、单位正方形、非标准单位和标准单位；③作图要点使用了GeoGebra命令如Zip, PointToPixels, Flatten, Sequence, centerBox, Polygon, Remove, IsInRegion, Element, If, Vector, Sort, Length, Corner等；④适合4-5年级学生，用于学习使用网格和标准单位确定矩形、正方形和组合图形的面积。

GeoGebra 命令及参数

  1. Zip(If[Mod[A, 10] ≟ 0, 20, 0] + Mod[A, 10] + ((9 - Div[A, 10]) * 10), A, filledIndex) → filledIndexReverse
  2. PointToPixels(Corner[1], Corner[3], Corner[5], startPt) → StartPixels
  3. Flatten(Sequence[Sequence[(Mod[A, gridMaxX], Mod[B, gridMaxY]), A, 0, gridMaxX - 1], B, 0, gridMaxY - 1]) → AllBoxPoints
  4. Zip(Element[AllBoxPoints, A], A, filledIndex) → filledBoxPoints
  5. Sequence(false, k, 1, 100) → falseList
  6. centerBox(boxWidth, boxHeight, moveablePt) → moveableBox
  7. centerBox(boxWidth, boxHeight, startPt) → startBox
  8. Polygon((0, 0) - (boxWidth / 2, boxHeight / 2), (gridMaxX, 0) - (boxWidth / 2, boxHeight / 2), (gridMaxX, gridMaxY) - (boxWidth / 2, boxHeight / 2), (0, gridMaxY) - (boxWidth / 2, boxHeight / 2)) → Region, f, g, h, i
  9. Remove(KeepIf[0 < x < (gridMaxX * gridMaxY) + 1, Unique[Flatten[Zip[If[Mod[A, 10] ≟ 1, {A + gridMaxX, A + 1, A - gridMaxX}, If[Mod[A, 10] ≟ 0, {A + gridMaxX, A - gridMaxX, A - 1}, {A + gridMaxX, A + 1, A - gridMaxX, A - 1}]], A, filledIndex]]]], filledIndex) → adjIndex
  10. Zip(Element[AllBoxPoints, A], A, adjIndex) → adjPoints
  11. Zip(Distance[A, closestIntPoint], A, adjPoints) → distanceList
  12. IsInRegion(moveablePt, Region) → inRegion
  13. Element(adjIndex, IndexOf[Min[distanceList], distanceList]) → minIndex
  14. If(currentIndex ≟ 0, startPt, Element[AllBoxPoints, currentIndex]) → endPoint
  15. Vector(moveablePt, endPoint) → TransVec
  16. centerBox(boxHeight, boxWidth, moveablePt + (animatePoint * (x(TransVec), y(TransVec)))) → movingBox
  17. Zip(If[A, "colorPurpleButton", "colorGreyInactiveButton"], A, boxList) → colorBoxes
  18. Remove(AllBoxPoints, filledBoxPoints) → greyBoxPoints
  19. Zip(centerBox[boxHeight, boxWidth, A], A, greyBoxPoints) → greyBoxes
  20. Zip(centerBox[boxHeight - gap, boxWidth - gap, A], A, filledBoxPoints) → filledBoxes
  21. Sequence(Segment[(((-boxWidth)) / 2, ((-boxHeight)) / 2) + (A * (boxWidth, 0)), (((-boxWidth)) / 2, gridMaxY - boxHeight / 2) + (A * (boxWidth, 0))], A, 1, gridMaxX - 1) → verticalLines
  22. Sequence(Segment[(((-boxWidth)) / 2, ((-boxHeight)) / 2) + (A * (0, boxHeight)), (((-boxWidth)) / 2 + gridMaxX, ((-boxHeight)) / 2) + (A * (0, boxHeight))], A, 1, gridMaxY - 1) → horizontalLines
  23. Sort(filledIndex, filledIndexReverse) → sortedFilledIndex
  24. Zip(Element[AllBoxPoints, A], A, Take[sortedFilledIndex, 1, fillArea]) → showAreaBoxPoints
  25. Zip(centerBox[boxHeight - gap, boxWidth - gap, A], A, showAreaBoxPoints) → showAreaFilledBoxes
  26. Length(filledIndex) → area
  27. Zip(centerBox[boxHeight, boxWidth, A], A, Remove[filledBoxPoints, showAreaBoxPoints]) → emptyBoxOutline
  28. Corner(5) → corner5
  29. onboardingTextOffset(Corner[onboardingText, 1], Corner[onboardingText, 3], 1, Corner[1], Corner[3], Corner[5]) → OnboardingTextOffset
  30. expandQuad(Vertex[moveableBox, 1], Vertex[moveableBox, 2], Vertex[moveableBox, 3], Vertex[moveableBox, 4], (7 * pulsing), Corner[1], Corner[3], Corner[5]) → pulsingSquare
  31. If(area ≟ 1, "", "s") → sText

AI 绘图提示语参考

在网格上绘制一个可交互的面积探索图形。网格由等宽等高的正方形单元格组成，覆盖一个矩形区域。部分单元格被填充为紫色，表示已选中的单位方块，其余为灰色。一个可拖动的方块用于选择或取消单元格，选中后填充区域会高亮显示。图形包含网格线、单元格轮廓以及一个显示当前选中面积的文本标签。整体用于演示矩形、正方形和组合图形的面积计算，支持通过拖动改变填充范围。
以上提示语为根据原始绘图命令整理而来，仅供参考。