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给定截面的立体图形 by Steve Phelps

给定截面的立体图形 by Steve Phelps
几何画板及绘图内容加载中，请稍等……
2019-03-06 06:48
立体几何微积分积分
这个范例展示了给定截面的立体图形。它涉及微积分中的积分概念，通过构造不同形状的截面来生成立体图形。使用了Point, IndexOf, CurveCartesian, Surface, Polygon, OrthogonalPlane, OrthogonalLine, CircleSector等GeoGebra命令。适合高中或大学微积分课程中的立体几何教学。

GeoGebra 命令及参数

  1. Point(xAxis) → A
  2. Point(xAxis) → B
  3. IndexOf(SelectedElement[shape], shape) → a
  4. CurveCartesian(t, g(t) + (f(t) - g(t)) / 2, ((f(t) - g(t)) / 2 * sqrt(3)), t, x(A), x(B)) → b
  5. Surface(t, (u * g(t)) + ((1 - u) * y(b(t))), ((1 - u) * z(b(t))), t, x(A), x(B), u, 0, 1) → c
  6. Surface(t, (u * f(t)) + ((1 - u) * y(b(t))), ((1 - u) * z(b(t))), t, x(A), x(B), u, 0, 1) → d
  7. CurveCartesian(t, f(t), f(t) - g(t), t, x(A), x(B)) → h
  8. CurveCartesian(t, g(t), f(t) - g(t), t, x(A), x(B)) → i
  9. Surface(t, f(t), (u * z(h(t))), t, x(A), x(B), u, 0, 1) → j
  10. Surface(t, g(t), (u * z(i(t))), t, x(A), x(B), u, 0, 1) → k
  11. Surface(t, (u * g(t)) + ((1 - u) * f(t)), z(i(t)), t, x(A), x(B), u, 0, 1) → l
  12. CurveCartesian(t, f(t), f(t) - g(t), t, x(A), x(B)) → m
  13. Surface(t, (u * g(t)) + ((1 - u) * f(t)), ((1 - u) * (f(t) - g(t))), t, x(A), x(B), u, 0, 1) → n
  14. Surface(t, f(t), ((1 - u) * (f(t) - g(t))), t, x(A), x(B), u, 0, 1) → o
  15. CurveCartesian(t, g(t), f(t) - g(t), t, x(A), x(B)) → p
  16. Surface(t, (u * f(t)) + ((1 - u) * g(t)), ((1 - u) * (f(t) - g(t))), t, x(A), x(B), u, 0, 1) → q
  17. Surface(t, g(t), ((1 - u) * (f(t) - g(t))), t, x(A), x(B), u, 0, 1) → r
  18. CurveCartesian(t, (f(t) + g(t)) / 2, 0, t, x(A), x(B)) → s
  19. Surface(t, y(s(t)) + ((f(t) - g(t)) / 2 * cos(u)), ((f(t) - g(t)) / 2 * sin(u)), t, x(A), x(B), u, 0, π) → t_1
  20. Polygon((t, g(t), 0), (t, f(t), 0), b(t)) → t1, e, f_1, g_1
  21. Polygon((t, f(t), 0), h(t), i(t), (t, g(t), 0)) → q1, h_1, i_1, j_1, k_1
  22. Polygon((t, f(t), 0), m(t), (t, g(t), 0)) → t2, l_1, m_1, n_1
  23. Polygon((t, f(t), 0), (t, g(t), 0), p(t)) → t3, p_1, q_1, r_1
  24. CurveCartesian(t, ((f(t) - g(t)) / 2 * cos(u)) + y(s(t)), ((f(t) - g(t)) / 2 * sin(u)), u, 0, π) → u
  25. OrthogonalPlane(C, xAxis) → v
  26. OrthogonalLine(C, v) → s_1
  27. Point(u) → D
  28. Point(u) → E
  29. CircleSector(C, D, E, xOyPlane) → c_1