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汤匙折叠的几何构造

汤匙折叠的几何构造
几何画板及绘图内容加载中，请稍等……
2016-11-03 00:42
三角函数微积分几何作图
①本范例演示了通过旋转和交点构造一个由汤匙折叠形成的几何图形；②涉及的核心数学概念包括分段函数、梯形、根、微积分和比例；③作图要点使用了PointIn, Segment, Point, Rotate, IntersectConic, Plane, Intersect, If, Polygon, Mirror, Distance, Circle, Ray等GeoGebra命令和对象；④适合高中及以上学生学习和理解复杂几何构造与微积分应用。

GeoGebra 命令及参数

  1. PointIn(o) → A
  2. Segment(((-x(A)), y(A)), (x(A) - y(A) - 0.01, y(A))) → nn
  3. Point(nn) → C
  4. Segment((Max[(-x(A)), x(Intersect[Circle[C, A], xAxis, 1])], 0), Intersect[Circle[C, A], xAxis, 2]) → jj
  5. Point(jj) → B
  6. Rotate(Polygon[{B, C, ((-x(A)), y(A)), ((-x(A)), 0)}], (pliage * π / 2), xAxis) → poly1
  7. Rotate(C, (pliage * π / 2), xAxis) → C'
  8. IntersectConic(Sphere[C', Distance[C, A]], Sphere[B, Distance[B, A]]) → c
  9. Plane(A, Plane[xAxis, zAxis]) → a
  10. Intersect(a, c) → D_1, D_2
  11. If(pliage ≟ 0, (x(A), y(A), 0), If[z(D_1) ≥ 0, D_1, D_2]) → D
  12. Polygon({B, C', D}) → poly2
  13. Polygon({B, D, Mirror[D, Plane[xAxis, zAxis]]}) → poly3
  14. Mirror(poly1, Plane[xAxis, zAxis]) → poly1'
  15. Mirror(poly2, Plane[xAxis, zAxis]) → poly2'
  16. Intersect(OrthogonalLine[B, Plane[C', D, Mirror[D, Plane[xAxis, zAxis]]]], Plane[C', D, Mirror[D, Plane[xAxis, zAxis]]]) → H
  17. Segment(B, H) → h
  18. Polygon({C', D, Mirror[D, Plane[xAxis, zAxis]]}) → poly4
  19. Polygon(A, ((-x(A)), y(A)), ((-x(A)), (-y(A))), (x(A), (-y(A)))) → poly5, a_1, f, g, i
  20. Distance(A, C) → distanceAC
  21. Circle(C, A) → d
  22. Segment(B, (x(A), 0)) → k
  23. Ray((x(D), 0, z(D)), (x(C'), 0, z(C'))) → l
  24. Circle(A, y(A)) → e
  25. Segment(B, A) → j
  26. Segment(B, C) → m
  27. Mirror(B, xAxis) → B'
  28. Mirror(A, xAxis) → A'
  29. Segment(B', A') → j'
  30. Mirror(B, xAxis) → B'_1
  31. Mirror(C, xAxis) → C'_1
  32. Segment(B'_1, C'_1) → m'
  33. Segment(((-x(A)), 0), (x(A), 0)) → n