球面上的圆 by Guillermo Bautista

几何画板及绘图内容加载中，请稍等……

2021-12-30 22:06

圆立体几何几何作图

所属专题 Curves and Spirals on Spheres

这个范例展示了球面上的圆。它涉及球面几何中的核心概念，通过使用GeoGebra的Sequence命令，可以动态地生成一系列圆。作图要点包括使用Sequence命令生成一系列半径和直径不同的圆。适合高中及以上学生或教师用于教学和研究。

GeoGebra 命令及参数

Sequence(CurveCartesian[((r * sin(u)) * cos(v)), ((r * sin(u)) * sin(v)), (r * cos(u)), u, 0, (2 * π)], v, 0, (2 * π), π / d) → list1, {(((3.2 * sin(u)) * cos(0)), ((3.2 * sin(u)) * sin(0)), (3.2 * cos(u))), (((3.2 * sin(u)) * cos(0.39269908169872414)), ((3.2 * sin(u)) * sin(0.39269908169872414)), (3.2 * cos(u))), (((3.2 * sin(u)) * cos(0.7853981633974483)), ((3.2 * sin(u)) * sin(0.7853981633974483)), (3.2 * cos(u))), (((3.2 * sin(u)) * cos(1.1780972450961724)), ((3.2 * sin(u)) * sin(1.1780972450961724)), (3.2 * cos(u))), (((3.2 * sin(u)) * cos(1.5707963267948966)), ((3.2 * sin(u)) * sin(1.5707963267948966)), (3.2 * cos(u))), (((3.2 * sin(u)) * cos(1.9634954084936207)), ((3.2 * sin(u)) * sin(1.9634954084936207)), (3.2 * cos(u))), (((3.2 * sin(u)) * cos(2.356194490192345)), ((3.2 * sin(u)) * sin(2.356194490192345)), (3.2 * cos(u))), (((3.2 * sin(u)) * cos(2.748893571891069)), ((3.2 * sin(u)) * sin(2.748893571891069)), (3.2 * cos(u))), (((3.2 * sin(u)) * cos(3.141592653589793)), ((3.2 * sin(u)) * sin(3.141592653589793)), (3.2 * cos(u))), (((3.2 * sin(u)) * cos(3.5342917352885173)), ((3.2 * sin(u)) * sin(3.5342917352885173)), (3.2 * cos(u))), (((3.2 * sin(u)) * cos(3.9269908169872414)), ((3.2 * sin(u)) * sin(3.9269908169872414)), (3.2 * cos(u))), (((3.2 * sin(u)) * cos(4.319689898685965)), ((3.2 * sin(u)) * sin(4.319689898685965)), (3.2 * cos(u))), (((3.2 * sin(u)) * cos(4.71238898038469)), ((3.2 * sin(u)) * sin(4.71238898038469)), (3.2 * cos(u))), (((3.2 * sin(u)) * cos(5.105088062083414)), ((3.2 * sin(u)) * sin(5.105088062083414)), (3.2 * cos(u))), (((3.2 * sin(u)) * cos(5.497787143782139)), ((3.2 * sin(u)) * sin(5.497787143782139)), (3.2 * cos(u))), (((3.2 * sin(u)) * cos(5.890486225480863)), ((3.2 * sin(u)) * sin(5.890486225480863)), (3.2 * cos(u))), (((3.2 * sin(u)) * cos(6.283185307179588)), ((3.2 * sin(u)) * sin(6.283185307179588)), (3.2 * cos(u)))}
Sequence(CurveCartesian[((r * sin(u)) * cos(v)), ((r * sin(u)) * sin(v)), (r * cos(u)), v, 0, (2 * π)], u, (-π), π, π / d) → list2, {(((3.2 * sin(-3.141592653589793)) * cos(v)), ((3.2 * sin(-3.141592653589793)) * sin(v)), (3.2 * cos(-3.141592653589793))), (((3.2 * sin(-2.748893571891069)) * cos(v)), ((3.2 * sin(-2.748893571891069)) * sin(v)), (3.2 * cos(-2.748893571891069))), (((3.2 * sin(-2.356194490192345)) * cos(v)), ((3.2 * sin(-2.356194490192345)) * sin(v)), (3.2 * cos(-2.356194490192345))), (((3.2 * sin(-1.9634954084936207)) * cos(v)), ((3.2 * sin(-1.9634954084936207)) * sin(v)), (3.2 * cos(-1.9634954084936207))), (((3.2 * sin(-1.5707963267948966)) * cos(v)), ((3.2 * sin(-1.5707963267948966)) * sin(v)), (3.2 * cos(-1.5707963267948966))), (((3.2 * sin(-1.1780972450961724)) * cos(v)), ((3.2 * sin(-1.1780972450961724)) * sin(v)), (3.2 * cos(-1.1780972450961724))), (((3.2 * sin(-0.7853981633974483)) * cos(v)), ((3.2 * sin(-0.7853981633974483)) * sin(v)), (3.2 * cos(-0.7853981633974483))), (((3.2 * sin(-0.39269908169872414)) * cos(v)), ((3.2 * sin(-0.39269908169872414)) * sin(v)), (3.2 * cos(-0.39269908169872414))), (((3.2 * sin(0)) * cos(v)), ((3.2 * sin(0)) * sin(v)), (3.2 * cos(0))), (((3.2 * sin(0.39269908169872414)) * cos(v)), ((3.2 * sin(0.39269908169872414)) * sin(v)), (3.2 * cos(0.39269908169872414))), (((3.2 * sin(0.7853981633974483)) * cos(v)), ((3.2 * sin(0.7853981633974483)) * sin(v)), (3.2 * cos(0.7853981633974483))), (((3.2 * sin(1.1780972450961724)) * cos(v)), ((3.2 * sin(1.1780972450961724)) * sin(v)), (3.2 * cos(1.1780972450961724))), (((3.2 * sin(1.5707963267948966)) * cos(v)), ((3.2 * sin(1.5707963267948966)) * sin(v)), (3.2 * cos(1.5707963267948966))), (((3.2 * sin(1.9634954084936207)) * cos(v)), ((3.2 * sin(1.9634954084936207)) * sin(v)), (3.2 * cos(1.9634954084936207))), (((3.2 * sin(2.356194490192345)) * cos(v)), ((3.2 * sin(2.356194490192345)) * sin(v)), (3.2 * cos(2.356194490192345))), (((3.2 * sin(2.748893571891069)) * cos(v)), ((3.2 * sin(2.748893571891069)) * sin(v)), (3.2 * cos(2.748893571891069))), (((3.2 * sin(3.141592653589793)) * cos(v)), ((3.2 * sin(3.141592653589793)) * sin(v)), (3.2 * cos(3.141592653589793)))}

AI 绘图提示语参考

在三维空间中画一个半径为3.2的球面，并在球面上生成一组圆；这些圆位于不同纬度截面中，每个圆的圆心都在球心沿法向方向对应的截面位置。用参数化方式让纬圈从u=0变化到u=2π，步长分成d等份（例如d=16），并在每一步以v从0到2π给出该圆上的点，从而形成一串随u变化的圆。再取另一组圆：让u从-π到π变化并同样按d等分，在每个u位置用v从0到2π描出对应的圆，用以展示球面上的交错圆环。

以上提示语为根据原始绘图命令整理而来，仅供参考。