花箱体积计算
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①本范例演示如何通过旋转二维图形计算花箱的体积;②涉及核心数学概念包括体积计算、旋转几何、函数与导数;③构造过程中运用了函数、线段、旋转、交点、角度、多边形、导数、根、最小值等GeoGebra命令与对象;④适合高中立体几何与微积分教学,用于可视化理解体积计算与空间变换。
GeoGebra 命令及参数
Function(((x * (length - (2 * x))) * (width - (2 * x))), 0, Vright) → VSegment(B, C) → bRotate(B, α, A) → B'Line(B', A) → sLine(Ax, s) → s1Segment(A, B) → aLine(C, a) → rIntersect(s, r) → DLine(Dy, r) → r1Intersect(r1, b) → CySegment(Dy, Cy) → c1Segment(C, D) → cIntersect(s1, c) → DxSegment(Ax, Dx) → d1Intersect(d1, c1) → D1Line(B, s) → qLine(Bx, q) → q1Intersect(q1, c) → CxSegment(Bx, Cx) → b1Intersect(b1, c1) → C1Line(A, B) → pLine(Ay, p) → p1Intersect(p1, b) → BySegment(Ay, By) → a1Intersect(d1, a1) → A1Intersect(b1, a1) → B1Angle(B, A, B') → βSegment(D, A) → dPolygon(A1, A2a, B2a, B1) → poly1, e, f, g, h_1Polygon(B1, B2b, C2b, C1) → poly2, i, j, k, lPolygon(C1, C2c, D2c, D1) → poly3, c_1, d_1, e_1, f_1Polygon(D1, D2d, A2d, A1) → poly4, m, n, a_1, b_1Derivative(V) → VderRoot(Vder) → tMax_1, tMax_2Min(x(tMax_1), x(tMax_2)) → tMaxSegment(tMax_1, P) → g_1Intersect(c1, d1) → EIntersect(c1, b1) → FIntersect(b1, a1) → GIntersect(d1, a1) → HPolygon(E, F, G, H) → poly5, e_2, f_2, g_2, h_2