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使用拼布图案计算组合图形面积

使用拼布图案计算组合图形面积
几何画板及绘图内容加载中，请稍等……
2022-11-16 10:14
测试改名0多边形解析几何几何作图
本范例通过分解拼布图案来计算组合图形的面积。涉及的核心数学概念包括三角形、平行四边形、梯形、圆以及组合图形的面积计算。作图要点使用了GeoGebra命令如Max, Element, Append, Join, Polygon, Rotate, Flatten, Zip, Mod, TableText, Sequence等来创建和操作图形。适合6-8年级学生，用于学习和实践几何图形面积的计算。

GeoGebra 命令及参数

  1. Max({Length[data1], Length[data2], Length[data3]}) → maxRows
  2. Max(0, maxRows - 1) → numZeros
  3. Element({"", "0", "00", "000", "0000", "00000", "000000", "0000000", "00000000", "000000000", "0000000000", "00000000000"}, numZeros + 1) → zeroStr
  4. Append(Sequence["\phantom{1}", A, 1, maxRows + 1], "Total Area") → col0
  5. Join({{(("\cellcolor{" * colorPURPLE) * "}{Purple}")}, Sequence[If[A ≤ Length[data1], ("~" * data1(A)), ""], A, 1, maxRows], {(If[Sum[data1] < 10, "~", ""] * Sum[data1])}}) → col1
  6. Join({{(("\cellcolor{" * colorORANGE) * "}{Orange}")}, Sequence[If[A ≤ Length[data2], ("~" * data2(A)), ""], A, 1, maxRows], {(If[Sum[data2] < 10, "~", ""] * Sum[data2])}}) → col2
  7. Join({{(("\cellcolor{" * colorGRAY) * "}{Gray}")}, Sequence[If[A ≤ Length[data3], ("\,\,\," * data3(A)), ""], A, 1, maxRows], {(If[Sum[data3] < 10, "\,\,\,", ""] * Sum[data3])}}) → col3
  8. Polygon({(1, 7), (1, 4), (2, 3), (2, 6), (3, 7)}) → poly11
  9. Polygon({(3, 6), (6, 6), (7, 5), (7, 7), (4, 7)}) → poly12
  10. Polygon({(1, 3), (1, 1), (4, 1), (5, 2), (2, 2)}) → poly13
  11. Polygon({(5, 1), (7, 1), (7, 4), (6, 5), (6, 2)}) → poly14
  12. Polygon({(2, 5), (3, 5), (4, 4), (3, 4)}) → poly15
  13. Rotate(poly15, (3 * pi / 2), (4, 4)) → poly16
  14. Rotate(poly15, pi, (4, 4)) → poly17
  15. Polygon({(2, 5), (4, 7), (5, 7), (4, 8), (2, 6)}) → poly21
  16. Rotate(poly21, ((-pi)) / 2, (4, 4)) → poly22
  17. Rotate(poly21, (-pi), (4, 4)) → poly23
  18. Rotate(poly21, pi / 2, (4, 4)) → poly24
  19. Rotate(poly15, pi / 2, (4, 4)) → poly18
  20. Polygon({(4, 4), (4, 5), (3, 6), (3, 5)}) → poly25
  21. Rotate(poly25, ((-pi)) / 2, (4, 4)) → poly26
  22. Rotate(poly25, pi, (4, 4)) → poly27
  23. Rotate(poly25, pi / 2, (4, 4)) → poly28
  24. Polygon({(0, 4), (0, 8), (4, 8), (3, 7), (1, 7), (1, 5)}) → poly31
  25. Rotate(poly31, ((-pi)) / 2, (4, 4)) → poly32
  26. Rotate(poly31, pi, (4, 4)) → poly33
  27. Rotate(poly31, pi / 2, (4, 4)) → poly34
  28. Polygon({(2, 3), (2, 5), (3, 4)}) → poly35
  29. Rotate(poly35, ((-pi)) / 2, (4, 4)) → poly36
  30. Rotate(poly35, pi, (4, 4)) → poly37
  31. Rotate(poly35, pi / 2, (4, 4)) → poly38
  32. Polygon({(2, 5), (3, 5), (3, 6)}) → poly39
  33. Rotate(poly39, ((-pi)) / 2, (4, 4)) → poly39b
  34. Rotate(poly39, pi, (3.9816581927706727, 3.9816581927706722)) → poly39c
  35. Rotate(poly39, pi / 2, (4, 4)) → poly39d
  36. Flatten(Sequence[Zip[Rotate[A, B, (4, 4)], A, {poly11, poly15, poly21, poly25, poly31, poly35, poly39}], B, 0, (3 * pi / 2), pi / 2]) → outlines
  37. Zip((("SetLayer(poly" * A) * ",4)"), A, polyNameExtensions) → cmdResetLayers
  38. Zip((("SetFixed(poly" * A) * ",true,true)"), A, polyNameExtensions) → cmdUnlockPieces
  39. Mod(outlineIndex, 7) → pieceType
  40. Element({0, 3, 0, 0, 0, 5, 0, 0}, pieceType + 1) → numSquares
  41. Element({1, 2, 2, 5, 2, 2, 2, 1}, pieceType + 1) → numTriangles
  42. Polygon({LegendAnchor, LegendAnchor + (1, 0), LegendAnchor + (1, 1), LegendAnchor + (0, 1)}) → legendSquare
  43. Polygon({LegendAnchor + (4, 0), LegendAnchor + (5, 0), LegendAnchor + (5, 1)}) → legendTriangle
  44. TableText(col0, col1, col2, col3, tableFormatStr) → dataTable
  45. Flatten(Sequence[Zip[Rotate[A, B, (4, 4)], A, {poly11, poly15}], B, 0, (3 * pi / 2), pi / 2]) → color1pieces
  46. Flatten(Sequence[Zip[Rotate[A, B, (4, 4)], A, {poly21, poly25}], B, 0, (3 * pi / 2), pi / 2]) → color2pieces
  47. Flatten(Sequence[Zip[Rotate[A, B, (4, 4)], A, {poly31, poly35, poly39}], B, 0, (3 * pi / 2), pi / 2]) → color3Pieces
  48. Sequence(true, i, 1, 28) → allCovers
  49. Join({Sequence[Segment[AnchorA + (i, 0), AnchorA + (i, 8)], i, 1, 7], Sequence[Segment[AnchorA + (0, i), AnchorA + (8, i)], i, 1, 7]}) → quiltGrid

AI 绘图提示语参考

绘制一个由多个几何图形组成的复合图形，包括三角形、平行四边形、梯形和圆形。首先绘制一个七边形，然后围绕一个中心点旋转多个小多边形，形成一个复杂的图案。最后，根据旋转角度和图形类型，将这些图形组合成一个完整的图案，计算并显示每个图形的面积。
以上提示语为根据原始绘图命令整理而来，仅供参考。