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AB2008_1c_B 体积与正方形截面

AB2008_1c_B 体积与正方形截面
几何画板及绘图内容加载中，请稍等……
2016-03-18 22:28
立体几何微积分积分几何作图滑块动画
①本范例演示通过旋转区域形成立体图形，并计算其体积，采用正方形截面方法；②涉及核心数学概念包括微积分中的体积计算、积分、极限、几何作图；③构造中运用了 Sequence（序列）、Intersect（交点）、Segment（线段）、Integral（积分）、Locus（轨迹）、Polygon（多边形）等 GeoGebra 命令；④适合高中微积分学习，用于理解旋转体体积计算方法。

GeoGebra 命令及参数

  1. Sequence(Polygon[(fI(((k + p) * h)), (k * h), 0), (gI(((k + p) * h)), (k * h), 0), (gI(((k + p) * h)), (k * h), ht(((k + p) * h))), (fI(((k + p) * h)), (k * h), ht(((k + p) * h)))], k, 0, m - 1) → SlicesFront
  2. Intersect(f, g, 3, 5) → E
  3. Segment(A, B) → e
  4. Integral((fI(x) - gI(x))^(2), 0, 3) → Integ
  5. Locus(C, s) → loc1
  6. If(togS ≟ 1, "Hide surface", "Show surface") → ShowSurface
  7. Locus(D, s) → loc2
  8. Polygon(A, B, C, D) → Rect, a, b, c, d
  9. Angle(B, A, D) → α
  10. Segment((0, 6, 27), (9, 6, 27)) → i
  11. If(togDF ≟ 1, "Show Directions", "Show volume integral") → ToggleDirectionVolumeIntegral
  12. Sequence(Area[Element[SlicesFront, k]], k, 1, m) → Areas
  13. Sequence(Surface[gI(((k + p) * h)), ((k + u) * h), (v * ht(((k + p) * h))), u, 0, 1, v, 0, 1], k, 0, m - 1) → SlicesLeft
  14. Sequence(Surface[(v * fI(((k + p) * h))) + ((1 - v) * gI(((k + p) * h))), ((k + u) * h), ht(((k + p) * h)), u, 0, 1, v, 0, 1], k, 0, m - 1) → SlicesTop
  15. Sequence(Polygon[(fI(((k + p) * h)), (k * h), 0), (gI(((k + p) * h)), (k * h), 0), (gI(((k + p) * h)), ((k + 1) * h), 0), (fI(((k + p) * h)), ((k + 1) * h), 0)], k, 0, m - 1) → SlicesBase
  16. Sequence(Polygon[(fI(((k + p) * h)), ((k + 1) * h), 0), (gI(((k + p) * h)), ((k + 1) * h), 0), (gI(((k + p) * h)), ((k + 1) * h), ht(((k + p) * h))), (fI(((k + p) * h)), ((k + 1) * h), ht(((k + p) * h)))], k, 0, m - 1) → SlicesBack
  17. Sequence(Surface[fI(((k + p) * h)), ((k + u) * h), (v * ht(((k + p) * h))), u, 0, 1, v, 0, 1], k, 0, m - 1) → SlicesRight
  18. Surface((v * fI(u)) + ((1 - v) * gI(u)), u, 0, u, 0, 3, v, 0, 1) → Base
  19. Surface((v * fI(u)) + ((1 - v) * gI(u)), u, ht(u), u, 0, 3, v, 0, 1) → Top
  20. Surface(fI(u), u, (v * ht(u)), u, 0, 3, v, 0, 1) → SurfaceFront
  21. Surface(gI(u), u, (v * ht(u)), u, 0, 3, v, 0, 1) → SurfaceBack