What does a 4D object look like

Grabbe-Gymnasium Detmold

Last change: August 5th, 2020, 7:49 pm

four-dimensional geometry


The hypercube


We cannot imagine a four-dimensional spatial object. We record the fourth dimension as duration in the apparently space-independent dimension "time". But we can correctly imagine an object projection into three-dimensional space. When a three-dimensional cube rotates under a light source over a sheet of paper, we see Rhytmically moving shadow image. For example a circular square if the light source is positioned exactly above the center of the cube. The rotating four-dimensional hypercube would create the object shown in the animation film as its physical shadow image, which does not cover a surface like the usual shadow images, but a 3D space segment The confusing transformation of inside and outside can usually not be observed in the movements of purely three-dimensional objects in space. It is an animation trick similar to the trick of perspective drawing to represent 3D objects on the drawing sheet. A 4D projection into our space would however in the Ta t look so confusing. But it is more likely that we would view such a projection as a sequence of apparently independent objects. A cube that looks like this replaces a cube that looks a little different. The 4D hypercube disintegrates into a sequence of 3D object views that emerge and fade and seemingly replace each other. But the whole sequence is really just a 4D object, no matter how long it takes.

Similar representations:

Curved space and rotation