Top Class Posters

Can you tell me about a cube in the 4th dimension?

I dont know much about this subject, but I find it fascainating. When I was in school, I remember my math teacher showing us this picture of a “shadow of a cube in the 4th dimension”. It made no sense to me, but amazed me at the same time. I know that the 4th dimension is Time, and I remember her saying that we could not possibly imagine what a cube in the 4th dimension would look like, but that this picture would be a “shadow” of one in the 4th dimension. Does anyone know anything at all about this subject and can enlighten me?

See this: http://en.wikipedia.org/wiki/Tesseract

Physicists commonly think of time as being the fourth dimension. However, according to string theory (which at this point has not been proven to be true) the Universe has 10 or 11 dimensions of space and one dimension of time.

A four-dimensional hypercube, often called a teesseract, is not “in the fourth dimension,” but occupies four dimensions. Similarly, we three-dimensional people are not “in the third dimension,” but we occupy all three dimensions at once.

While we cannot gain the perspective of the fourth dimension to view a tesseract, we can get an appreciation of what it looks like by looking at projections (like your teacher showed you) and animations of projections. The projection of a 4-D object into 3-D space is 3-D. A 4-D object can also be projected into 2-D and 1-D space. Think of the drawing of a regular 3-D cube on a sheet of paper (2-D projection).

This is a good visualization where you can click and drag the 2-D projection of a tesseract to look at it from differen angles. If it were possible to make a wireframe tesseract and hold it at arms length while you rotated it in 4-D, this is what you would see:

http://www.geocities.com/hjsmithh/WireFrame4/tesseract.html

This one doesn’t let you control it, but it is better at showing one rotation in 4-D:

http://www.math.harvard.edu/archive/21b_fall_03/4dcube/index.html

You might take a look at these:

http://www.weimholt.com/andrew/tesseract.html

http://www.well.com/~abs/SIGGRAPH96/4Dtess.html

And here is a Google search: http://linkwrap.com/4259

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