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AP_2014_2a 数学范例

AP_2014_2a 数学范例
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2017-06-30 03:12
所属专题 Volumes in AP Calculus
①本范例演示了特殊点、均值、二项分布、极限和等腰三角形的几何与概率关系；②涉及核心数学概念包括特殊点计算、均值定理、二项分布模型、极限求解、等腰三角形性质；③构造过程中运用了 GeoGebra 命令 Sequence（数列）、Polygon（多边形）、Rotate（旋转）、Integral（积分）、Surface（曲面）、RectangleSum（矩形和）；④适合高中及以上数学学习，用于理解高等数学与几何的结合应用。

GeoGebra 命令及参数

  1. Sequence(Polygon[((k * h), f(((k + p) * h))), (((k + 1) * h), f(((k + p) * h))), (((k + 1) * h), g(((k + p) * h))), ((k * h), g(((k + p) * h)))], k, 0, m - 1) → Rectangles
  2. Polygon(((DK * h), f(((DK + p) * h))), (((DK + 1) * h), f(((DK + p) * h))), (((DK + 1) * h), g(((DK + p) * h))), ((DK * h), g(((DK + p) * h)))) → Rectangle1, b, c, d, e
  3. Rotate(Rectangle1, (-α), a) → Rectangle1'
  4. Integral((π * ((2 + g(x))^(2) - (2 + f(x))^(2))), 0, 2.3) → VolInteg
  5. Rotate(Rectangles, (-α), a) → Rectangles'
  6. Rotate(g_1, (-α), a) → i
  7. Rotate(f_1, (-α), a) → j
  8. Surface(u, -2 + ((2 + f(((DK + p) * h))) * cos(β)), ((2 + f(((DK + p) * h))) * sin(β)), u, (DK * h), ((DK + 1) * h), β, 0, α) → Inner1
  9. Surface(u, -2 + ((2 + g(((DK + p) * h))) * cos(β)), ((2 + g(((DK + p) * h))) * sin(β)), u, (DK * h), ((DK + 1) * h), β, 0, α) → Outer1
  10. Surface((DK * h), -2 + ((u + 2) * cos(β)), ((u + 2) * sin(β)), u, f(((DK + p) * h)), g(((DK + p) * h)), β, 0, α) → SideLeft1
  11. Surface(((DK + 1) * h), -2 + ((u + 2) * cos(β)), ((u + 2) * sin(β)), u, f(((DK + p) * h)), g(((DK + p) * h)), β, 0, α) → SideRight1
  12. Surface(u, -2 + ((2 + f(u)) * cos(β)), ((2 + f(u)) * sin(β)), u, 0, 2.3, β, 0, (2 * π)) → InnerSurf
  13. Surface(u, -2 + ((2 + g(u)) * cos(β)), ((2 + g(u)) * sin(β)), u, 0, 2.3, β, 0, (2 * π)) → OuterSurf
  14. Sequence(Surface[u, -2 + ((2 + f(((k + p) * h))) * cos(β)), ((2 + f(((k + p) * h))) * sin(β)), u, (k * h), ((k + 1) * h), β, 0, α], k, 0, m - 1) → Inners
  15. Sequence(Surface[u, -2 + ((2 + g(((k + p) * h))) * cos(β)), ((2 + g(((k + p) * h))) * sin(β)), u, (k * h), ((k + 1) * h), β, 0, α], k, 0, m - 1) → Outers
  16. Sequence(Surface[(k * h), -2 + ((u + 2) * cos(β)), ((u + 2) * sin(β)), u, f(((k + p) * h)), g(((k + p) * h)), β, 0, α], k, 0, m - 1) → SidesLeft
  17. Sequence(Surface[((k + 1) * h), -2 + ((u + 2) * cos(β)), ((u + 2) * sin(β)), u, f(((k + 1 + p) * h)), g(((k + 1 + p) * h)), β, 0, α], k, 0, m - 1) → SidesRight
  18. RectangleSum(A, 0, (m * h), m, p) → WS