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半圆截面的几何构造

半圆截面的几何构造
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2016-08-12 07:14
圆积分几何作图
这个范例展示了半圆截面的几何构造。涉及的核心数学概念包括圆和相似三角形。通过使用GeoGebra命令如Semicircle、Sequence和Integral，可以动态地展示半圆截面的形成过程。适合高中几何和微积分课程使用。

GeoGebra 命令及参数

  1. Segment(A, B) → e
  2. Integral((π / 2 * r(x)^(2)), -2, 2) → Integ
  3. If(togDF ≟ 1, "Show Instructions", "Show volume integral") → ToggleDirectionVolumeIntegral
  4. If(togS ≟ 1, "Hide surface", "Show surface") → ShowSurface
  5. Plane((0, 0, 0), (0, 1, 1), (0, 2, 0)) → a
  6. Surface(u, (v * f(u)) + ((1 - v) * g(u)), 0, u, -2, 2, v, 0, 1) → Base
  7. Semicircle(A, B, a) → SC
  8. Sequence(Surface[u, c(-2 + ((k + p) * h)) + (r(-2 + ((k + p) * h)) * cos(β)), (r(-2 + ((k + p) * h)) * sin(β)), u, -2 + (h * k), -2 + ((k + 1) * h), β, 0, π], k, 0, m - 1) → SlicesTop
  9. Sequence(Semicircle[(-2 + (k * h), g(-2 + ((k + p) * h)), 0), (-2 + (k * h), f(-1 + ((k + p) * h)), 0), a], k, 0, m - 1) → SlicesLeft
  10. Sequence(Semicircle[(-2 + ((k + 1) * h), g(-2 + ((k + p) * h)), 0), (-2 + ((k + 1) * h), f(-1 + ((k + p) * h)), 0), a], k, 0, m - 1) → SlicesRight
  11. Sum(Sequence[((h * π / 8) * (g(-2 + ((k + p) * h)) - f(-2 + ((k + p) * h)))^(2)), k, 0, m - 1]) → VolSlices
  12. Sequence(Polygon[(-2 + (k * h), f(-2 + ((k + p) * h))), (-2 + (k * h), g(-2 + ((k + p) * h))), (-2 + ((k + 1) * h), g(-2 + ((k + p) * h))), (-2 + ((k + 1) * h), f(-2 + ((k + p) * h)))], k, 0, m - 1) → SlicesBase
  13. Surface(u, c(u) + (r(u) * cos(β)), (r(u) * sin(β)), u, 0, 2, β, 0, π) → TopRight
  14. Surface(u, c(u) + (r(u) * cos(β)), (r(u) * sin(β)), u, -2, 0, β, 0, π) → TopLeft