# Talk:Three-dimensional space

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## 2d=3d

It's said that a 3D object is several 2D objects stacked on-top of each-other to create thickness but how can several 2D planes with a thickness of 0 add up to be something that has thickness and thus create a 3D object?

Because you're stacking together an uncountably infinite number of 2D objects. Infinity times 0 is not necessarily 0 (technically, it's undefined). Crispy (talk) 00:43, 26 March 2009 (UTC)

## 3d networks as spaces

This article may be improved by adding a mention of Graphs (ie networks of nodes or connectivity information) that have dimension of 3 through Dimensional_analysis. This type of structure is an alternative to the axis-based way of thinking about the dimensionality of space in the universe. See also Fractal dimension on networks. Danwills (talk) 03:51, 12 November 2008 (UTC)

The article would benefit from a link to Dimensional analysis, and but I don't think this application of dimensional analysis belongs in the article. --Una Smith (talk) 01:39, 2 July 2009 (UTC)

## SVG Drawing

The article's first picture is badly in need of proper formatting to get rid of the "jaggies". I suggest conversion to SVG. - KitchM (talk) 21:44, 10 October 2009 (UTC)

## Hypersphere

This space is above (in dimension) the sphere or the 2-sphere:

If the 2-sphere lives in her own but also can be viewed embedded in ${\displaystyle \mathbb {R} ^{3}}$ and is defined as ${\displaystyle p\in \mathbb {R} ^{3}}$ such that ${\displaystyle p=(x,y,z)^{\perp }}$ and ${\displaystyle x^{2}+y^{2}+z^{2}=1}$.

And the hypersphere -very well known to a real topo-geometer- is: a set consisting of point in the 4-dimensional euclidean space ${\displaystyle \mathbb {R} ^{4}}$ which are equidistant to the origin, usually we take distance one. In other words: ${\displaystyle p\in \mathbb {R} ^{4}}$ such that, if ${\displaystyle p=(x,y,z,t)^{\perp }}$ then ${\displaystyle x^{2}+y^{2}+z^{2}+t^{2}=1}$. So, i don't know why unsavvy geeks think they know and write lies, and only producing that math look stupid... well, that it seems a law in these wikiplaces. --kmath (talk) 22:28, 25 September 2011 (UTC)

Anyway not all is lost: check 3-sphere for education--kmath (talk) 22:37, 25 September 2011 (UTC)
Huh? Hypersphere refers to any number of dimensions, though n-sphere is a more common synonym. Indeed the former is sometimes restricted to 3 or more dimensions, but here we already state explicitly that n = 2. Double sharp (talk) 13:20, 28 August 2013 (UTC)

Just as a 3D object casts a 2D shadow (kinda) should it be noted that a theoretical 4D (not time) object would cast a 3D shadow? (kinda.) or is this all too original researchy? 74.132.249.206 (talk) 11:13, 15 October 2011 (UTC)

That wouldn't be about 3D, it would be about 4D. And there's already something at Four-dimensional space saying that. Dmcq (talk) 11:59, 15 October 2011 (UTC)

As a submersions of a 4-manifold into a 3-manifolds, in fact locally watching close the case R^4->R^3, worth to know, thinka--kmath (talk) 18:29, 31 October 2011 (UTC)

## Undid Vandalism, but ...

I undid some clear vandalism, but have no idea what the article is supposed to look like. I just did this 'en passant' and have other things I must do. Can some Samaritan look this over? DeepNorth (talk) 14:16, 11 November 2012 (UTC)

## Merger proposal

This article should be merged with space as that article is also explicitly dedicated to three-dimensional space.Rgdboer (talk) 22:26, 5 November 2013 (UTC)

Nah, space focuses more on space in physics, that is, the spacetime with time held constant. This page is about a mathematical ideal, does not put physics and reality into account. In mathematics there are 4-dimensional space or n-dimensional, this page is for n=3. We collects its mathematical property, insights and geometries here. --14.198.220.253 (talk) 20:47, 28 November 2013 (UTC)
I propose that we add a "for physical space, see space." redirect (something like that) and fix the leading paragraph, ie. put the description on physics a little bit lower than the mathematical description.
A section and paragraphs on the significance of 3-dimensional space in physics, and a redirect to space for detailed article. --14.198.220.253 (talk) 20:57, 28 November 2013 (UTC)
Really late oppose, but I don't want this merged. I have the same reasons as "14.198.220.253", in that this is a mathematical... thing. For example, four-dimensional space doesn't focus at all on the effects of physics, just a mathematical... thing. Pikachu Bros. (talk) 17:36, 19 March 2014 (UTC)

Yes, I see your point: parts of the other page having reference to physicality would not apply to this page. The WP:namespace logic is clear, and have taken down the merger tags. Thank you for clearing that up; three dimensions need not be materialized.Rgdboer (talk) 02:08, 24 March 2014 (UTC)

### 2nd merger

@Rgdboer and Pikachu Bros.: Titles of articles should reflect their content. So I'd like to rename the present article to Three-dimensional space (mathematics), which is already tagged as the main page of section Space#Mathematics; then redirect Three-dimensional space to the broader-concept primary-topic page about three-dimensional space in general (physical, mathematical, etc.), which is the Space article. Fgnievinski (talk) 21:15, 25 June 2015 (UTC)

I've renamed the article, split the two small non-mathematical sections into Space, but stopped shy of retargeting the redirect Three-dimensional space to Space, as most current incoming links seem to be deal with mathematics. Fgnievinski (talk) 02:53, 29 June 2015 (UTC)

## Length, width, height, depth and ..... breadth?... what?

What exactly is Breadth? I know an 3 dimensional object top-down has depth and a 3 dimensional object looked at sideways has height... But what is breadth? Breadth and Length both point to the same article called "Length". I find that sentence very unclear. please clarify it. 195.177.247.202 (talk) 14:37, 7 August 2014 (UTC)

Since three dimensions is three dimensions whichever way you look at it, you can call the dimensions anything you want. Older textbooks called them width, breadth, and height. They would show a picture of a rectangle, with the distance from side to side labeled width and the distance from top to bottom labeled breadth. The idea was that we were looking down on the rectangle from above, and the third dimension, height, came up out of the page. More modern textbooks usually assume the rectangle is standing up in front of us. The distance from side to side is still width, but now they call the distance from bottom to top height, and the distance a three dimensional object extends behind the rectangle depth. If you think this important enough to put in the article, I'll try to find a reference. Rick Norwood (talk) 14:55, 7 August 2014 (UTC)

A three dimensional object can be described by:

• LENGTH is used for the greater of the two horizontal dimensions. If there is not a clear top and bottom, length is the greatest of the three dimensions.
• WIDTH is used for the dimension between sides which have a degree of mirror-image symmetry, such as left and right, or two sides of a flowing river.
• HEIGHT is used for the vertical above-surface dimension, or the dimension which would be vertical if the object were upright.
• DEPTH is used for cavities, measured from side of normal view or access to opposite, such as the depth of a lake from top surface to bottom, or depth of a cupboard from front surface (door) to back.
• THICKNESS is the smallest dimension.
• DIAMETER is the dimension across the circle a solid or hollow object that is more-or-less cylindrical (soup can) or spherical (ball)
• SPREAD is the dimension across the circle a granular object that is more-or-less cylindrical or spherical, such as collections of leaves on a tree or buildings in a city.

Usually one of those is a good fit for each of your dimensions. Sometimes two fit, in which case you get to make a choice. Sometimes none fit, in which case you should use breadth.

• BREADTH is not the greatest nor smallest dimension, (at least, not significantly largest or smallest,) not from left to right, nor near to far, nor bottom to top, but whatever is left over.

A loaf of bread, for example, has length, breadth and height; while a slice of bread has thickness, breadth and height. — Preceding unsigned comment added by 64.178.132.12 (talk) 05:43, 22 April 2015 (UTC)

## What's wrong with the diagram at the top?

The top diagram has a note which says "(See diagram description for correction.)" Why does it need correction? It looks okay to me. Either the diagram should be corrected or the parenthetical note should be deleted. Wahrmund (talk) 16:10, 16 January 2016 (UTC)

The image is the standard depiction of the coordinate axes that we have all gotten use to, which is why it looks okay. The "correction" that the note refers to is that a "real" set of orthogonal coordinates projected into a plane wouldn't actually look like that. This is due to the fact that if you don't want the x-axis to come directly out towards the viewer (and therefore be invisible) you have to rotate around the z-axis. This rotation causes the right angle of the yz-quadrant to not appear as a right angle to the viewer. The objection is legitimate, which is probably why the comment hasn't been removed, but in my mind it is pretty pedantic. We could probably get away with a caption that indicated that the image was just a "representation" of the axes. Bill Cherowitzo (talk) 19:59, 16 January 2016 (UTC)
Okay, I have inserted "representation." If other editors object, I am sure they will change it back. Wahrmund (talk) 20:12, 16 January 2016 (UTC)

## Proposal: Revert article title to Three-dimensional space

I propose that the title of this article be reverted to three-dimensional space for the following reasons:

1. The article title should be consistent with other similar articles: zero-dimensional space, one-dimensional space, two-dimensional space, four-dimensional space, five-dimensional space, six-dimensional space, seven-dimensional space, and eight-dimensional space. See also: Template:Dimension topics.
2. According to Special:WhatLinksHere/Three-dimensional space (mathematics), the largest number of incoming links (500 links at the present time) are redirects from three-dimensional space.

Please discuss. If there is consensus to revert the name, I think an admin may have to do it. Biogeographist (talk) 16:23, 3 August 2016 (UTC)

Counter-proposal: rename Space to Three-dimensional space. fgnievinski (talk) 20:25, 3 August 2016 (UTC)
Agree. The “(mathematics)“ is pointless and non-standard disambiguation. There is no other “three-dimensional space“ that it needs disambiguating from, as can be seen by the redirect from three-dimensional space. As for Space that is a broader summary of the topic, including physical models with more than thee dimensions, so it is definitely not just three-dimensional.--JohnBlackburnewordsdeeds 20:42, 3 August 2016 (UTC)
It seems to me (and to JohnBlackburne in the preceding comment) that Space includes non-mathematical meanings (geographical and psychological), whereas this article, like all the articles on n-dimensional space (all the rest of which lack the parenthetical disambiguation), focus on mathematics. Thanks for the responses. Biogeographist (talk) 01:40, 4 August 2016 (UTC)
Three-dimensional space currently redirects to Space which is also the target of Physical space. This is the most common, concrete meaning. The abstract mathematical meaning is secondary. fgnievinski (talk) 16:13, 4 August 2016 (UTC)
I think you are mistaken; Three-dimensional space redirects to Three-dimensional space (mathematics), as far as I can see, because you moved Three-dimensional space to Three-dimensional space (mathematics). Could you explain why you think the article name of three-dimensional space should be treated differently from zero-dimensional space, one-dimensional space, two-dimensional space, four-dimensional space, five-dimensional space, six-dimensional space, seven-dimensional space, and eight-dimensional space? Because currently I cannot see a good reason why it should be treated differently. Please take a look at those articles and let me know what you think. Thanks, Biogeographist (talk) 21:18, 4 August 2016 (UTC)
Looks like I left the move unfinished. I did mean to retarget the redirect Three-dimensional space to Space, the eveyday concept that most people are familiar with. Higher dimensional spaces are more esoteric and need no disambiguation because their main conceptualization is mathematical indeed. But the most common concept for 3D space is the tactile one, not its mathematical theorization. fgnievinski (talk) 21:40, 4 August 2016 (UTC)
I think you may have forgotten what you wrote above a year ago, where you said: "I've renamed the article, split the two small non-mathematical sections into Space, but stopped shy of retargeting the redirect Three-dimensional space to Space, as most current incoming links seem to deal with mathematics." According to that comment, you did not forget to redirect Three-dimensional space to Space; you chose not to redirect for what seems to me to be a good reason. Do you have any sources to support the idea that "the most common concept for 3D space is the tactile one"? In his 1946 book Art & Geometry: A Study in Space Intuitions, William Ivins, Jr. argued that the most common concept for 3D space was the tactile one for the ancient Greeks, but I am not sure that is true today. It's plausible that it's true, I just don't have reliable sources at hand to confirm or disconfirm the idea. But in any case, as you noted in your comment from last year, "most current incoming links seem to deal with mathematics." So I am still of the mind that Three-dimensional space is the most appropriate name for the article (but I am open to hear further evidence to the contrary). Biogeographist (talk) 00:47, 5 August 2016 (UTC)

Alright, please go ahead with reverting the renaming, but let's leave the hatnote in place, indicating that the present article is not meant to cover everything about three dimensional space, e.g., for non mathematical aspects, please see Space. fgnievinski (talk) 03:57, 5 August 2016 (UTC)

Sounds good. I will use the requested move template. Biogeographist (talk) 14:37, 5 August 2016 (UTC)

## Requested move 5 August 2016

The following is a closed discussion of a requested move. Please do not modify it. Subsequent comments should be made in a new section on the talk page. Editors desiring to contest the closing decision should consider a move review. No further edits should be made to this section.

The result of the move request was: Moved (non-admin closure) — Andy W. (talk ·ctb) 17:15, 13 August 2016 (UTC)

Three-dimensional space (mathematics)Three-dimensional space – Parenthetical disambiguation was added to the article title last year during a content merge, but discussion on the talk page has concluded that the parenthetical disambiguation is not necessary; among other reasons, the largest number of incoming links are redirects from Three-dimensional space. See discussion on the talk page above this template for further reasons. Biogeographist (talk) 14:49, 5 August 2016 (UTC)

• support. As above, but restating the "(mathematics)" is unnecessary and so non-standard disambiguation – there is no other article called three-dimensional space.--JohnBlackburnewordsdeeds 15:34, 5 August 2016 (UTC)
• Support, although I had to put on my 3-D glasses to read the nom. Also, the other 0-eight dimensional space pages all go without the "mathematics" descriptor, so it seems for consistency that this page can be moved without the RM. Randy Kryn 17:39, 5 August 2016 (UTC)
• Support. BTW, it's not necessary to use full RM to remove unnecessary disambiguation when there is no other article competing for the same title; just use the speedy process at WP:RM#TR.  — SMcCandlish ¢ ≽ʌⱷ҅ʌ≼  05:33, 7 August 2016 (UTC)
• Strong support – Would have snow-closed this but I'm feeling cautious tonight JFG talk 02:35, 12 August 2016 (UTC)

The above discussion is preserved as an archive of a requested move. Please do not modify it. Subsequent comments should be made in a new section on this talk page or in a move review. No further edits should be made to this section.