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Mathematics B‑class High‑priority

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1. prior to August 2006
2. August 2006 - Nov 11

Lost Cube?

During an analysis of the tesseract "folding" .gif, I noticed that only 7 3-Dimensional figures seem to exist in the tesseract seen in the pictures on the page: 6 truncated square pyramids warped from cubes, and one cube in the center. That infers the erroneous "destruction" of one cube, that, at least in my eyes, is impossible and therefore proves the tesseract an invalid 4-dimensional shape.

Could someone clear this up for me? Thanks. - This Is M4dn355 300 (talk) 02:27, 13 March 2012 (UTC)

I don't know which figure you are referring to. If you click on a picture you will see its name. However from your description it sounds to me that you have not included the outside which is another cube just like the inside one. It may look outside in the 3d projection but is a cube face just like the others in 4d. Hope that's what you're talking about. Dmcq (talk) 11:34, 13 March 2012 (UTC)

This is the only "folding gif" I know about, comparing folding a tesseract and a cube. Tom Ruen (talk) 22:03, 13 March 2012 (UTC)

That's the folding .gif I was looking at, however, I've noticed it in every picture I've looked at. Dmcq, does this mean there are two cubes? If so, I think it is necessary to mention in the article, as some users such as myself may be confused. - This Is M4dn355 300 (talk) 00:00, 14 March 2012 (UTC)

There are eight cubes bounding the tesseract. Each cube touches six other cubes and has an opposite cube. In 3d a cube has six faces and each face touches four other faces and has an opposite face. Dmcq (talk) 00:11, 14 March 2012 (UTC)

I understand that from looking at the .gif. My question is what happens after folding it. There are 6 truncated square pyramids formed from the 6 cubes immediately surrounding the one at the intersection of the 3 lines formed by the cubes of the 3D representation of a cross (no better name for that :/ ). Since there only seems to be 1 cube in the apparent center of the larger cube, it seems to me that there're only 7 cubes at the end of the process.

From your explanation, it seems to me that there are two cubes where there seems to be only one, one actually being on the outside. Is this correct, and if not, please explain where the 8th cube (farthest from the "center" on the longest arm) goes.

I said prior that the article needs to elaborate on this, as many users such as myself won't understand this. Can a better 2D representation of this be created or is the outside cube (if what I'm saying is correct) always facing towards the viewer? - This Is M4dn355 300 (talk) 02:40, 14 March 2012 (UTC)

I don't know what 'it' in 'I have noticed it in every picture I have looked at' refers to. I don't know what 'this' in your last paragraph refers to.

You have referred to 'in the centre of the larger cube'. The larger cube on the outside is the eight cube. Can you count the six squares in the 3D picture? If you look at the picture of a cube in 3D you will see that the sixth square is on the outside in that picture. The large cube is the closest in 4D just like the outside square is the closest in 3D. The small cube is the furthest away one in 4D just like the the small square is the back square in the 3D picture. If we had an opaque tesseract we'd only see the big cube, the third picture under perspective projection shows an opaque tesseract projected to 3D and one can only see four cubes in that. Dmcq (talk) 09:02, 14 March 2012 (UTC)

I'm not referring to what it would look like in 3D. Forget what I've said previously. Where does the bottommost cube (from the .gif) go?

It's circled in this rather crappy image (Imageshack's new registration rule -.-): http://desmond.imageshack.us/Himg24/scaled.php?server=24&filename=2000pxtesseract2svg.png&res=medium

- This Is M4dn355 300 (talk) 15:46, 14 March 2012 (UTC)

Aahh... I understand now. Thank you for attempting to help me understand this. - This Is M4dn355 300 (talk) 16:10, 14 March 2012 (UTC)

Wrinkle In Time

There was a reference to Tesseract in the children's Sci-Fi book "A Wrinkle in Time". Perhaps worth a mention? Thnx! -HK — Preceding unsigned comment added by 24.1.233.206 (talk) 22:24, 26 June 2012 (UTC)

There's a continual battle on adding and removing "cultural/literary/art" references. It looks like the current battle lines stand at none of them. A while ago I made a copy on the talk page, now at Talk:Tesseract/Archive_2#Tesseracts_in_popular_culture. Tom Ruen (talk) 22:44, 26 June 2012 (UTC)

The 'tesseract' in a wrinkle in time is not the same as the tesseract described in this article. The only connection is someone decided to use a cool word. Too trivial to include unless some secondary source makes some sort of meaningful linkage. Dmcq (talk) 23:52, 26 June 2012 (UTC)

Actually I missed seeing it, but it is listed at Tesseract#See_also. Tom Ruen (talk) 00:24, 27 June 2012 (UTC)

Change arrow to point up

In the diagram showing how to get from dimension 0 to 4, just change the green arrow to point up instead of down. That way, we're always moving in a positive direction. Thanks. — Preceding unsigned comment added by 99.254.2.209 (talk) 02:24, 6 July 2012 (UTC)

Retrieving "Tesseracts"?

At the moment "Tesseracts" redirects to "Tesseract" but there is a series of science fiction anthologies named "Tesseracts". If I were to create a page for it, how would I keep it from redirecting here? Monado (talk) 01:20, 9 April 2013 (UTC)

If you enter "Tesseracts" in the search page, you will be directed to this page, but you will see a small note at the top that says "(Redirected from Tesseracts)". If you click on the Tesseracts link in that note, you will get the redirect page, which you can then edit. It might be best to title your article something like "Tessaracts (magazine)" and make the Tessaracts article a disambiguation page that points here and to your article. Leave me a note on my talk page if you need more help.--agr (talk) 03:20, 9 April 2013 (UTC)

About image in Tesseract article

Re:User_talk:David_Eppstein#About_image_in_Tesseract_article and the comment...

So may I consider consensus is reached and I may add image again? Rawal of Jaisalmer (talk) 08:40, 4 June 2013 (UTC)

No, we can't so quickly come to that conclusion.

I understand your frustration, as I too have been edited off this island with actual 4D rotation matrix dot product algorithm produced comparative static (and animations) of nD (in this case 4 for the 8-cube Tesseract) to 3D (and 2D as well). I do both perspective and parallel orthographic, normal 3D and stereoscopic 3D projections. I have never seen yours (but will try the Isometric_projection transformation matrix and check it out with my code.

I disagree with your suggestion that the Schlegel projection is more artifical as "2 steps". The way you describe it sounds like you are doing it by hand. If you actually do the math to project nD objects (which I do), it is really all about proper projections from 3 nD basis vectors (for 3D projections), the transformation matrices, and defining of the camera (eye) location.

If this is indeed a true projection (and not simply a hand drawn model - that may be in error), what basis vectors are used on the vertices of the 8 cell in order to project to that image. Do you have the code to do that?

Jgmoxness (talk) 13:58, 5 June 2013 (UTC)

I also still feel the image shouldn't be here, bevause (1) there are already too many images, and I don't understand what this is supposed to bring thatt the others don't, and (2) despite repeated questions on my talk page, I still did not get a clear explanation of exactly what principle was used to construct this image and what it is supposed to mean. The lack of continued discussion on my talk was me getting frustrated and not continuing to ask the same questions that had already been not answered before, it was not agreement. —David Eppstein (talk) 16:00, 5 June 2013 (UTC)

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