平面与积分的交互演示

几何画板及绘图内容加载中，请稍等……

2015-08-23 01:14

微积分积分

①本范例演示了平面、积分与切线的交互关系，通过动态调整参数观察几何图形的变化；②涉及的核心数学概念包括平面、几何分布、切线、积分计算、内切圆；③作图要点使用了Surface（曲面）、Sequence（数列）等GeoGebra命令，以及对象a, h, U, V, UU, b, d, n, liste1, liste2；④适合高中及以上学生学习和理解微积分、几何作图等知识点。

GeoGebra 命令及参数

Surface(((cos(u) * cos(v)) * cos((a * v))) - (sin((a * v)) * (sin(v) + h)), (sin(u) * cos(v)), ((cos(u) * cos(v)) * sin((a * v))) + (cos((a * v)) * (sin(v) + h)), u, π - UU, π + UU - U, v, -1.5708, V) → b
Surface(((cos(u) * cos(v)) * cos((a * v))) - (sin((a * v)) * (sin(v) + h)), (sin(u) * cos(v)), ((cos(u) * cos(v)) * sin((a * v))) + (cos((a * v)) * (sin(v) + h)), u, 0.01 + π - UU, π + UU - U, v, -1.5708, V) → d
Sequence(CurveCartesian[((cos(u) * cos(v)) * cos((a * v))) - (sin((a * v)) * (sin(v) + h)), (sin(u) * cos(v)), ((cos(u) * cos(v)) * sin((a * v))) + (cos((a * v)) * (sin(v) + h)), u, π - UU, π + UU - U], v, -1.5708, V, π / n) → liste1
Sequence(CurveCartesian[((cos(u) * cos(v)) * cos((a * v))) - (sin((a * v)) * (sin(v) + h)), (sin(u) * cos(v)), ((cos(u) * cos(v)) * sin((a * v))) + (cos((a * v)) * (sin(v) + h)), v, -1.5708, V], u, π - UU, π + UU - U, (2 * π / n)) → liste2