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截面法体积可视化问题

截面法体积可视化问题
几何画板及绘图内容加载中，请稍等……
2017-03-11 02:56
函数解析几何立体几何微积分
①本范例演示通过截面法计算不规则体积的图形现象；②涉及核心数学概念包括体积计算、解析几何、积分、函数图像与几何作图；③作图要点提炼自构造摘要，使用了Intersect（相交）、Sequence（数列）等GeoGebra命令及对象n, g, f, C, D, b, a, A, s, square, isoscelesright1, isoscelesright2, equilateraltriangle, trapezoids, circles_revolutions, semicircles；④适合高中及以上学段，用于立体几何与微积分教学及可视化理解。

GeoGebra 命令及参数

  1. Intersect(f, g) → C, D
  2. Intersect(f, g, 1) → A
  3. Sequence(Polygon[(i, f(i), 0), (i, g(i), 0), (i, g(i), f(i) - g(i)), (i, f(i), f(i) - g(i))], i, a, b, s) → square
  4. Sequence(Polygon[(i, f(i), 0), (i, g(i), 0), (i, g(i) + (f(i) - g(i)) / 2, (0.5 * (f(i) - g(i))))], i, a, b, s) → isoscelesright1
  5. Sequence(Polygon[(i, f(i), 0), (i, g(i), 0), (i, g(i), f(i) - g(i))], i, a, b, s) → isoscelesright2
  6. Sequence(Polygon[(i, f(i), 0), (i, g(i), 0), (i, g(i) + (f(i) - g(i)) / 2, (sqrt(3) / 2 * (f(i) - g(i))))], i, a, b, s) → equilateraltriangle
  7. Sequence(Polygon[(i, f(i), 0), (i, g(i), 0), (i, g(i) + (0.25 * (f(i) - g(i))), (0.5 * (f(i) - g(i)))), (i, g(i) + (0.75 * (f(i) - g(i))), (0.5 * (f(i) - g(i))))], i, a, b, s) → trapezoids
  8. Sequence(Circle[(i, f(i), 0), (i, g(i), 0), (i, g(i) + (0.5 * (f(i) - g(i))), (0.5 * (f(i) - g(i))))], i, a, b, s) → circles_revolutions
  9. Sequence(Arc[Circle[(i, f(i), 0), (i, g(i), 0), (i, g(i) + (0.5 * (f(i) - g(i))), (0.5 * (f(i) - g(i))))], (i, g(i)), (i, f(i))], i, a, b, s) → semicircles

AI 绘图提示语参考

绘制一个立体图形，通过在x轴上从a到b区间内，依次绘制不同形状的横截面来构建。首先绘制一系列正方形，接着是等腰直角三角形，然后是等边三角形，之后是梯形，最后是半圆。每个形状的底边都在x轴上，高度随函数f(x)和g(x)变化，形成一个复杂的立体图形。
以上提示语为根据原始绘图命令整理而来，仅供参考。