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

Question

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?

Answer 1

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

Answer 2

First of all, the fourth dimension is only time in special relativity theory. When you speak of a general hypercube, the fourth dimension can be anything.
Since you cannot draw a hypercube in our three-dimensional space, you have to draw a projection (or shadow) of it. It's the same problem when you want to draw a cube onto a sheet of paper. You cannot draw the real cube, you can only draw a two-dimensional shadow of it. Since the hypercube is four-dimensional, you can project it into three dimensions, but also into two dimensions (like onto the computer screen). When you search the web for "hypercube" you should get some nice animated versions of this shadow, so you can get a better imagination of the hypercube.
I hope this helped.

Answer 3

A cube in 4 dimensions is actually called a "hypercube". By our understanding, when body casts a shadow, it loses a dimension (like the shadow of an airplane on the ground). So the shadow of a hypercube is a cube. Don't bother with trying to imagine it. The vast majority of humans (and in my opinion, everyone) would find it impossible.

Answer 4

you've requested an exciting question because believe it or no longer humanity is stepping into the Fourth measurement today and may end this flow by technique of 2012 (even as the Mayan calender ends). mom Earth is rushing up and subsequently all sorts of quirky issues are happening everywhere in the globe. The fourth measurement expertise is a a lot larger one than our element 3 expertise. each and absolutely everyone's wondering will be international and under no circumstances ethnic, nationalistic, provincial, and so on. you'll nevertheless have karma to do in spite of the indisputable fact that. you'll eliminate the demons on your subconscious and change into better angelic on your wondering and habit. only once you get to the fifth measurement will you be rid of that. Get those books: EARTH, THE COSMOS and also you, THE HATHOR textile, NEW TEACHINGS FOR AN AWAKENING HUMANITY.

Answer 5

I opine that a cube in the forth dimension is the set of cubes arranged side by side in the form of a line.
ie. A` Point' is dimensionless, `line' is mono dimensional, `area' is bi-dimensional and `cube' is tri-dimensional, moreover `line of cubes' is 4th-dimensional,..... in the same way we can assume nth-dimensional figure, since dimension is a notion created for our convenience to understand nature around us.

Answer 6

It is called a hypercube. I find the topic interesting as well. Here are some links:

http://uoregon.edu/~koch/hypersolids/hypersolids.html

http://www.harmwal.nl/hypercube/

There are also spheres and other things in the fourth dimension from what I understand. I hope this helped. :)