# From how many viewing angles does a tesseract look like a cube? **URL:** \ **Category:** Factual Questions\ **Created:** [February 13, 2013, 1:29am UTC](https://boards.straightdope.com/t/from-how-many-viewing-angles-does-a-tesseract-look-like-a-cube/650138 "2013-02-13T01:29:00Z")\ **Posts on this page:** 7\ **Page:** 1
**Author:** ![petew83](https://avatars.discourse-cdn.com/v4/letter/p/7bcc69/32.png) [@petew83](https://boards.straightdope.com/u/petew83)\ **Post date:** [February 13, 2013, 1:29am UTC](https://boards.straightdope.com/t/from-how-many-viewing-angles-does-a-tesseract-look-like-a-cube/650138/1 "2013-02-13T01:29:00Z")
I had the following thought today: A line can be viewed as a point from 2 angles. A square can be viewed as a line from 4 angles. A cube can be viewed as a square from 6 angles. Does this mean that a tesseract can be viewed as a cube from 8 angles? To test this out I need to find a good interactive tesseract. ---
**Author:** ![Andy\_L](https://avatars.discourse-cdn.com/v4/letter/a/c67d28/32.png) [@Andy\_L](https://boards.straightdope.com/u/Andy_L)\ **Post date:** [February 13, 2013, 1:40am UTC](https://boards.straightdope.com/t/from-how-many-viewing-angles-does-a-tesseract-look-like-a-cube/650138/2 "2013-02-13T01:40:15Z")
> [@petew83](#): > > I had the following thought today: > > A line can be viewed as a point from 2 angles. > A square can be viewed as a line from 4 angles. > A cube can be viewed as a square from 6 angles. > Does this mean that a tesseract can be viewed as a cube from 8 angles? > > To test this out I need to find a good interactive tesseract. Think of it this way. A line is bound by 2 endpoints, so there are two angles to look at the line so that you see only the endpoints. Similarly, a square is bounded by four lines, a cube by 6 squares, and a tesseract by 8 cubes, so you’re correct -there are eight angles to look at a hyper cube from, so that you see only the bounding cubes. ---
**Author:** ![stuyguy](https://avatars.discourse-cdn.com/v4/letter/s/ec9cab/32.png) [@stuyguy](https://boards.straightdope.com/u/stuyguy)\ **Post date:** [February 13, 2013, 2:26am UTC](https://boards.straightdope.com/t/from-how-many-viewing-angles-does-a-tesseract-look-like-a-cube/650138/3 "2013-02-13T02:26:27Z")
> [@petew83](#): > > A square can be viewed as a line from 4 angles. This is not correct. It looks like a line (segment) from many, many angles. ---
**Author:** ![petew83](https://avatars.discourse-cdn.com/v4/letter/p/7bcc69/32.png) [@petew83](https://boards.straightdope.com/u/petew83)\ **Post date:** [February 13, 2013, 4:36am UTC](https://boards.straightdope.com/t/from-how-many-viewing-angles-does-a-tesseract-look-like-a-cube/650138/4 "2013-02-13T04:36:48Z")
> [@](#): > > so you’re correct -there are eight angles to look at a hyper cube from, so that you see only the bounding cubes. So what cube angle do the eight ways look like? ---
**Author:** ![Andy\_L](https://avatars.discourse-cdn.com/v4/letter/a/c67d28/32.png) [@Andy\_L](https://boards.straightdope.com/u/Andy_L)\ **Post date:** [February 13, 2013, 1:00pm UTC](https://boards.straightdope.com/t/from-how-many-viewing-angles-does-a-tesseract-look-like-a-cube/650138/5 "2013-02-13T13:00:58Z")
> [@Andy\_L](#): > > Think of it this way. A line is bound by 2 endpoints, so there are two angles to look at the line so that you see only the endpoints. Similarly, a square is bounded by four lines, a cube by 6 squares, and a tesseract by 8 cubes, so you’re correct -there are eight angles to look at a hyper cube from, so that you see only the bounding cubes. I’ve reconsidered this answer: In two dimensional space, there are two angles you can look at a line and see only a point - but in three-dimensional (and higher) spaces there are an infinite number of angles that you can look at a line and see only a point. That infinite number of angles falls into two sets and you can continuously rotate from any angle in each of those sets to another angle in that set, without leaving the set. I suspect similar caveats need to be added to all the other cases as well. ---
**Author:** ![BigT](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/bigt/32/12044_2.png) [@BigT](https://boards.straightdope.com/u/BigT)\ **Post date:** [February 14, 2013, 3:09am UTC](https://boards.straightdope.com/t/from-how-many-viewing-angles-does-a-tesseract-look-like-a-cube/650138/6 "2013-02-14T03:09:19Z")
> [@stuyguy](#): > > This is not correct. It looks like a line (segment) from many, many angles. Most of us can see in three dimensions, and thus, if any corner is visible, would be able to see two lines moving away from a point in the Z dimension. ---
**Author:** ![SayTwo](https://avatars.discourse-cdn.com/v4/letter/s/e56c9b/32.png) [@SayTwo](https://boards.straightdope.com/u/SayTwo)\ **Post date:** [February 15, 2013, 8:13am UTC](https://boards.straightdope.com/t/from-how-many-viewing-angles-does-a-tesseract-look-like-a-cube/650138/7 "2013-02-15T08:13:11Z")
> [@Andy\_L](#): > > I’ve reconsidered this answer: In two dimensional space, there are two angles you can look at a line and see only a point - but in three-dimensional (and higher) spaces there are an infinite number of angles that you can look at a line and see only a point. That infinite number of angles falls into two sets and you can continuously rotate from any angle in each of those sets to another angle in that set, without leaving the set. > > I suspect similar caveats need to be added to all the other cases as well. True, but I see no reason to allow for this trivial case. If there is something to be gained from saying that there are only two ways to in 3D see a 2D line as a point, so be it.