Draw a 4-dimensional object in 3-dimensional space,can we?
周三, 07/07/2010 - 08:14 — 谢亚军
As we all know , we can draw a 3-dimensional 0bject in a 2-dimensional blackbold.
so the question is as follow:
why can't we draw a 4-dimensional object in 3-dimensional space?
评论
geometry and algebra
1-dimension: x=r, r can be minus
2-dimension: x=r cosα, y=r sinα, r could be, but needn't be, minus
3- dimension: x=r cosα sinθ, y=r sinα sinθ, z=r cosθ
4-dimension: x=r cosα sinθ sinλ, y=r sinα sinθ sinλ, z=r cosθ sinλ, i=r cosλ
...
以投影面为坐标面，如果只是投影，则只需把最后一维去掉即可；如果要算累积，那就积分。
3维到2维，投影面为xy平面，去掉z轴
2维到1维，投影面为x直线，去掉y轴
4维到3维，投影面为xyz体，去掉i轴
……