Obviously shadow is a 2 dimensional 
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Shadow is two dimensional because it calls on a screen
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If you think of a shadow as the lack of light created by an object blocking a light source, then shadows are 3-D. After all, it’s dark everywhere behind an object, not just on the surface of another object. Is a shadow the dark volume behind stuff, or the dark surface on other things?
If, on the other hand, you define a shadow to be what we see and intuitively think of (the dark, parroting person on the wall, with whom you can shadow box) and not the volume in between, then shadows are 2-D.