绘制对称多边形

绘制对称多边形
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2022-09-01 19:25
本范例演示如何通过镜像对称点来绘制对称多边形。核心数学概念包括对称性和多边形。使用GeoGebra命令如Rotate、Polygon、PointIn等进行多边形的构造。适合小学四年级至五年级学生学习对称性识别和绘制。

GeoGebra 命令及参数

  1. Element({0°, 90°, 45°}, caseNum) → rotAngle
  2. Rotate(xAxis, rotAngle) → axis
  3. Polygon({(min, min), (min, max), (max, max), (max, min)}) → viewbox
  4. PointIn(viewbox) → P1
  5. PointIn(viewbox) → P2
  6. PointIn(viewbox) → P3
  7. PointIn(viewbox) → P4
  8. PointIn(viewbox) → P5
  9. PointIn(viewbox) → P6
  10. PointIn(viewbox) → P7
  11. Shuffle({-5, -1}) → randomX5, {-1, -5}
  12. Element({0, Element[randomX5, Mod[countQuestion, Length[randomX5]] + 1], 0}, caseNum) → x5
  13. Shuffle({-1, -1, -1, -1, -2, -2, -2, -2, -3, -3, -3, -3, -4, -4, -4, -4}) → randomX, {-2, -2, -2, -1, -1, -4, -4, -2, -3, -1, -3, -4, -4, -3, -3, -1}
  14. Element(randomX, Mod[(4 * countQuestion) + 3, Length[randomX]] + 1) → x4
  15. Element(randomX, Mod[(4 * countQuestion) + 2, Length[randomX]] + 1) → x3
  16. Element(randomX, Mod[(4 * countQuestion) + 1, Length[randomX]] + 1) → x2
  17. Element(randomX, Mod[(4 * countQuestion), Length[randomX]] + 1) → x1
  18. Zip(Mirror[A, axis], A, givenPoints) → expectedResult
  19. Zip(A ≟ B, A, expectedResult, B, studentPoints) → correctCheck1
  20. Zip(A ≟ B, A, expectedResult, B, Reverse[studentPoints]) → correctCheck2
  21. If(reverseOrder, Reverse[correctCheck2], correctCheck1) → correctFinal
  22. If(reverseOrder, Reverse[studentPoints], studentPoints) → studentOrderedPoints
  23. Flatten(Zip[{x(A), y(A)}, A, studentPoints]) → inputCurrent
  24. Polygon(Element[{{(min, min), (min, 0), (max, 0), (max, min)}, {(0, min), (0, max), (max, max), (max, min)}, {(min, min), (max, max), (max, min)}}, caseNum]) → correctRegion
  25. Zip(IsInRegion[A, correctRegion], A, studentPoints) → regionCheck
  26. Polygon(Zip[PixelsToPoint[Corner[1], Corner[3], Corner[5], A], A, {(pixelsLeft, pixelsTop), (pixelsLeft, y(Corner[5]) - pixelsBottom), Corner[5] - (pixelsRight, pixelsBottom), (x(Corner[5]) - pixelsRight, pixelsTop)}]) → borderBox
  27. Corner(5) → layoutAppSize
  28. expandCircle(P1, 7 + haloPixels, Corner[1], Corner[3], Corner[5]) → pulsingObject
  29. PolyLine(givenPoints) → givenPattern
  30. PolyLine(expectedResult) → expectedPattern
  31. Zip(If[(¬A) ∧ (¬B) ∧ tries > 0, {228 / 255, 68 / 255, 97 / 255}, {101 / 255, 87 / 255, 210 / 255}], A, correctFinal, B, pointMoved) → pointColor
  32. PolyLine(studentPoints) → studentPattern
  33. Sequence((A, -5), A, -4, 3) → startPoints
  34. Zip(Vector[A, B], B, If[correctFinal ≟ correctCheck1, expectedResult, Reverse[expectedResult]], A, studentPoints) → moveVecs
  35. Zip(A + (animate * B), A, studentPoints, B, moveVecs) → movePoints
  36. PolyLine(movePoints) → animateAns
  37. Polygon({(min - 0.5, min - 0.5), (min - 0.5, max + 1), (max + 1, max + 1), (max + 1, min - 0.5)}) → coverScreen
  38. Sequence((((((("SetFixed(P" * A) * ",") * correctFinal(A)) * ",!") * correctFinal(A)) * ")"), A, If[reverseOrder, Length[studentPoints], 1], If[reverseOrder, 1, Length[studentPoints]], If[reverseOrder, -1, 1]) → cmdLockPoints
  39. Sequence((("SetFixed(P" * A) * ",false,true)"), A, 1, Length[studentPoints]) → cmdUnlockPoints
  40. RemoveUndefined(Zip[If[A, B], A, correctFinal, B, studentPoints]) → correctPoints
  41. Polygon({(min, min), (min, max), (max, max), (max, min)}) → viewBorder
  42. Sequence((("SetFixed(P" * A) * ",true,false)"), A, 1, Length[studentPoints]) → cmdLockAll

AI 绘图提示语参考

绘制一个对称多边形,例如正方形或矩形,通过镜像给定点来创建对称图形。图形包含一个矩形作为基础区域,多边形以及点在矩形内的标记。学生需要识别对称轴并绘制对称图形,同时检查点是否在多边形内部。构造顺序为:先创建矩形,再通过镜像操作生成对称点,最后验证点与多边形的关系。
以上提示语为根据原始绘图命令整理而来,仅供参考。