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?

周日, 09/05/2010 - 08:30 — Mike3224

Nikoidcuexfhtdjxou sglqsmrnyvn

周日, 09/05/2010 - 08:29 — Mike3224

hi there

周四, 07/08/2010 - 14:08 — puresky0

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

……

周四, 07/08/2010 - 04:59 — kambrian

well, that's what projection does,right?

and since you already have 2-D projection, the simplest way is to just add the additional dimension and problem solved.

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