圆锥的展开图 by Cuemath (2)

几何画板及绘图内容加载中，请稍等……

2019-01-10 18:54

①本范例演示了圆锥的展开图（扇形）的形成与计算；②涉及的核心数学概念包括立体几何、圆、角度、旋转、几何作图；③作图要点提炼自构造摘要，使用了正交线、圆、点、交点、圆锥、线段、距离、角度、旋转、圆周弧、曲面、笛卡尔曲线等GeoGebra命令/对象；④适合高中阶段学习立体几何、几何作图的学生使用。

GeoGebra 命令及参数

OrthogonalLine((1, 0, 0), xOyPlane) → a
Circle(a, (0, 0, 0)) → c
Point(a) → A
Intersect(xAxis, a) → B
Cone(B, A, 1) → b, d, e
Intersect(yAxis, xAxis) → C
Segment(C, A) → l
Distance(B, C) → r
Angle(A, C, B) → α
Rotate(A, (t * α), yAxis) → A'
OrthogonalLine(A', xOyPlane) → f
Intersect(f, xOyPlane) → B'
Rotate(C, β / 2, f) → C'
Rotate(C, ((-β)) / 2, f) → C'_1
CircumcircleArc(C', C, C'_1) → g
Distance(A', B') → h
Distance(B', C') → r'
Surface(((k - ((v * r') * cos((u * β / 2)))) * cos(ϕ)) - (((1 - v) * h) * sin(ϕ)), ((v * r') * sin((u * β / 2))), (((1 - v) * h) * cos(ϕ)) + ((k - ((v * r') * cos((u * β / 2)))) * sin(ϕ)), u, -1, 1, v, 0, 1) → j
CurveCartesian(((k - (r' * cos((u * β / 2)))) * cos(ϕ)), (r' * sin((u * β / 2))), ((k - (r' * cos((u * β / 2)))) * sin(ϕ)), u, -1, 1) → m
Segment(E, F) → n
Segment(D, F) → p