In a freshers lecture of

3-D geometry, our teacher said that3-Dobjects can be viewed as projections of4-Dobjects. How does this helps us visualize4-Dobjects?

I searched that we can at least see their3-Dcross-sections. ATesseracthypercube would be a good example.

Can we conclude that a 3-D cube is a shadow of a 4-D tesseract?But, how can a shadow be

3-D? Was the screen used for casting shadow also3-D; or else, what way is it different from basic physics of shadows we learnt?

edit:The responses are pretty good for4thdimensional analysis, but can we generalize this projection idea forndimensions, i.e. allndimensional objects will haven-1dimensional projections?

This makes me think abouthigher dimensionsdiscussed instring theory.

What other areas ofMathematicswill be helpful?

**Answer**

The animations below accompany an introductory talk on high-dimensional geometry.

Mathematically, the second was made by putting a “light source” at a point (0, 0, 0, h) (with h > 0) and sending each point (x, y, z, w) (with w < h) to \frac{h}{h - w}(x, y, z).

**Attribution***Source : Link , Question Author : pooja somani , Answer Author : Andrew D. Hwang*