圆与垂心关系演示

几何画板及绘图内容加载中，请稍等……

2016-12-23 04:13

所属专题 My 3D Collection

①本范例演示了圆、垂心与单位圆之间的关系，通过动态交互展示几何性质；②涉及核心概念包括圆、垂心、单位圆、树状图和割线；③作图要点提炼自构造摘要，使用了Surface（曲面）、R（点）、r（半径）、p、q、j、i、b、a、c、d、e、f、g、h等GeoGebra命令/对象；④适合高中及以上数学学习者，用于理解解析几何与几何作图的结合应用。

GeoGebra 命令及参数

Surface((2 * R) - i + ((R + r + (r * cos(u)^(1 / p))) * cos(v)^(1 / q)), (r * sin(u)^(1 / p)), (-2 * R) + r + i + ((R + (r * cos(u)^(1 / p))) * sin(v)^(1 / q)), u, 0, (2 * π), v, 0, (2 * π)) → b
Surface(((R + r + (r * cos(u)^(1 / p))) * cos(v)^(1 / q)), ((R + (r * cos(u)^(1 / p))) * sin(v)^(1 / q)), (-R) - r - j + (r * sin(u)^(1 / p)), u, 0, (2 * π), v, 0, (2 * π)) → a
Surface((3 * R) - r - (2 * i) + (r * sin(u)^(1 / p)), ((R + (r * cos(u)^(1 / p))) * sin(v)^(1 / q)), ((R + r + (r * cos(u)^(1 / p))) * cos(v)^(1 / q)), u, 0, (2 * π), v, 0, (2 * π)) → c
Surface(((R + r + (r * cos(u)^(1 / p))) * cos(v)^(1 / q)), ((R + (r * cos(u)^(1 / p))) * sin(v)^(1 / q)), R + r + j + (r * sin(u)^(1 / p)), u, 0, (2 * π), v, 0, (2 * π)) → d
Surface((2 * R) - i + ((R + r + (r * cos(u)^(1 / p))) * cos(v)^(1 / q)), (r * sin(u)^(1 / p)), (2 * R) - r - i + ((R + (r * cos(u)^(1 / p))) * sin(v)^(1 / q)), u, 0, (2 * π), v, 0, (2 * π)) → e
Surface((-2 * R) + i + ((R + r + (r * cos(u)^(1 / p))) * cos(v)^(1 / q)), (r * sin(u)^(1 / p)), (-2 * R) + r + i + ((R + (r * cos(u)^(1 / p))) * sin(v)^(1 / q)), u, 0, (2 * π), v, 0, (2 * π)) → f
Surface((-3 * R) + r + (2 * i) + (r * sin(u)^(1 / p)), ((R + (r * cos(u)^(1 / p))) * sin(v)^(1 / q)), ((R + r + (r * cos(u)^(1 / p))) * cos(v)^(1 / q)), u, 0, (2 * π), v, 0, (2 * π)) → g
Surface((-2 * R) + i + ((R + r + (r * cos(u)^(1 / p))) * cos(v)^(1 / q)), (r * sin(u)^(1 / p)), (2 * R) - r - i + ((R + (r * cos(u)^(1 / p))) * sin(v)^(1 / q)), u, 0, (2 * π), v, 0, (2 * π)) → h