带孔圆环体构造

几何画板及绘图内容加载中，请稍等……

2019-04-08 03:22

①本范例演示了一个三维带孔圆环体的构造与可视化；②涉及核心数学概念包括立体几何、圆、三角函数、向量与参数方程；③作图要点提炼自构造摘要，使用了Segment, Point, Max, Min, Line, Vector, Length, Surface, CurveCartesian, Sequence, Circle, Textfield等GeoGebra命令与对象；④适合高中及以上学生及数学爱好者用于学习立体几何与参数化建模。

GeoGebra 命令及参数

Segment((0, 0, π / 2), (0, 0, ((-π)) / 2)) → segInfSup
Point(segInfSup) → P2
Point(segInfSup) → P1
Max(z(P1), z(P2)) → vMax
Min(z(P1), z(P2)) → vInf
Point(yAxis) → A
Line(A, A + (1, 0, 0)) → rOp2
Point(rOp2) → B
Vector(A, B) → v2
Length(v2) → r1
Vector(A) → v
Length(v) → r
Surface((((cos((s * f(t))) * r1) * cos(t)) + (sin((s * f(t))) * r), (((-sin((s * f(t)))) * r1) * cos(t)) + (cos((s * f(t))) * r), (r1 * sin(t))), t, vInf, vMax, s, 0, (2 * π / n)) → parteSuperficie
CurveCartesian(((r1 * cos(t)), r, (r1 * sin(t))), t, (-π), π) → circ1T
Sequence(Rotate[circ1T, ((t * 360 / n))°, zAxis], t, 0, n - 1) → Circ
Sequence(Rotate[parteSuperficie, ((t * 360 / n))°, zAxis], t, 0, n - 1) → sup
Circle((0, 0, r1), r, zAxis) → Tapa1
Textfield(n) → CasillaDeEntrada1
Vector(P1) → vA
Vector(P2) → vB