两平行四边形间直角三角形截面体积计算

几何画板及绘图内容加载中，请稍等……

2015-07-02 12:42

所属专题 intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve intersection: surface-surface, curve-curve Volumes in Calculus Volumes in Calculus

本范例演示了如何计算两个平行四边形之间由直角三角形截面形成的体积。涉及的核心数学概念包括积分、立体几何和直角三角形性质。构造过程中使用了Polygon（多边形）、Angle（角）、Locus（轨迹）、Integral（积分）、If（条件判断）、Surface（曲面）、Sequence（数列）等GeoGebra命令和对象。适合高中及以上学生学习和理解体积计算方法，以及积分在几何中的应用。

GeoGebra 命令及参数

Polygon(B, A, C) → Triangle, c_1, b_1, a_1
Angle(B, A, C) → α
Locus(C, a) → loc1
Integral((4 + (2 * x) - (2 * x^(2)))^(2), -1, 2) → Integ
If(togDF ≟ 1, "Show Instructions", "Show volume integral") → ToggleDirectionVolumeIntegral
If(togS ≟ 1, "Hide surface", "Show surface") → ShowSurface
Surface(u, (v * f(u)) + ((1 - v) * g(u)), 0, u, -1, 2, v, 0, 1) → Base
Surface(u, g(u), ((2 * v) * (g(u) - f(u))), v, 0, 1, u, -1, 2) → SurfaceBack
Surface(u, (v * f(u)) + ((1 - v) * g(u)), (2 * ((v * f(u)) + ((1 - v) * g(u)) - f(u))), v, 0, 1, u, -1, 2) → SurfaceFront
Sequence(Polygon[(-1 + (k * h), f(-1 + ((k + p) * h))), (-1 + (k * h), g(-1 + ((k + p) * h))), (-1 + ((k + 1) * h), g(-1 + ((k + p) * h))), (-1 + ((k + 1) * h), f(-1 + ((k + p) * h)))], k, 0, m - 1) → SlicesBase
Sequence(Polygon[(-1 + (k * h), f(-1 + ((k + p) * h)), 0), (-1 + (k * h), g(-1 + ((k + p) * h)), 0), (-1 + (k * h), g(-1 + ((k + p) * h)), ht(-1 + ((k + p) * h)))], k, 0, m - 1) → SidesLeft
Sequence(Polygon[(-1 + ((k + 1) * h), f(-1 + ((k + p) * h)), 0), (-1 + ((k + 1) * h), g(-1 + ((k + p) * h)), 0), (-1 + ((k + 1) * h), g(-1 + ((k + p) * h)), ht(-1 + ((k + p) * h)))], k, 0, m - 1) → SidesRight
Sequence(Surface[-1 + ((k + u) * h), (v * g(-1 + ((k + p) * h))) + ((1 - v) * f(-1 + ((k + p) * h))), (v * ht(-1 + ((k + p) * h))), u, 0, 1, v, 0, 1], k, 0, m - 1) → SlicesTop
Sequence(Surface[-1 + ((k + u) * h), g(-1 + ((k + p) * h)), (v * ht(-1 + ((k + p) * h))), u, 0, 1, v, 0, 1], k, 0, m - 1) → SlicesBack
Sequence(Area[Element[SidesLeft, k]], k, 1, m) → Areas