Talk:Parallelepiped
From Wikipedia, the free encyclopedia
Contents |
[edit] Volume
This is partially copied, and reformatted, from a contrib by User:68.81.113.23 02:50, 2005 May 7 at User talk:Jerzy#parallelepiped (now at User talk:Jerzy/parallelepiped in its full context):
- If you mean to say "altitude of one of the faces, times the altitude of the parallelepiped", they try using those words. Your definition of the volume of a parallelepiped was and is incorrect....
(It refers to my edit on the article.)
The IP is correct, and i was wrong; my 3-D visualization skill is limited, and would not deserve exercise here at all if we could get more attention to such articles from those best equipped to edit them.
I think the language they intend to suggest is probably
- The volume of a parallelepiped is the product of the length of any edge, the length of the corresponding altitude of a face that includes it, and the length of the parallelepiped's altitude relative to that face.
But
- I'm feeling a bit cautious (overcautious, probably) about having it visualized perfectly,
- i'm even less confident about this somewhat common-sense terminoology being kosher (even tho i consider it unambiguous), and
- while i think we need to start with a method that does not appeal to either trig or vector-algebra techniques, i would like to encourage a confident editor to include a trig-oriented version, hopefully as a supplement somewhat like my own near-afterthought,
- Where the available facilities provide for it, this can be calculated most easily using the determinants, or equivalently via the scalar triple product or cross products.
(While i dislike anyone telling a WP editor what to work on, i've little doubt the IP i speak of would do better than i at visualizing and specifying the two angles (am i right in saying two?) whose sines are required, or the three whose sines are probably needed to express that sine in terms of angles between faces of the figure.)
--Jerzy (t) 00:09, 2005 May 8 (UTC)
- I think the formulation with the two altitudes is a bit confusing, as one of them is an altitude of a parallelogram while the other one is an altitude of the parallelepiped. So I replaced it with the IMHO more useful formula volume = base * height. However, a formulation in terms of the length of the edges and the angles of the parallelograms is probably also worth mentioning. -- Jitse Niesen 11:27, 9 May 2005 (UTC)
[edit] Relation with cubes
In the article it states "...is a three-dimensional figure like a cube, except that its faces are not squares...". However it is common practice in mathematics to have inclusive definitions, and this statement excludes a cube from being a parallelepiped, and excludes its faces being squares. I, however, would say a cube is just a specialized case of a parallelepiped, and that a face can be square. Who agrees? MathsIsFun 00:00, 18 January 2007 (UTC)
- Agreed. Indeed, even a cube is, according to that article, a type of "rectangular parallelepiped"... I'll reword here to rectify this apparent contradiction, i.e., by saying that the faces are "not necessarily" cubes or something to that effect. --Kinu t/c 14:17, 25 April 2007 (UTC)
[edit] Picture
I removed the picture shown on the right from the article. I agree with the IP editor who changed the article today that it is rather misleading, as the picture appears to show the height lying inside one of the faces, while in fact it should go through the body of the parallelepiped so that it is perpendicular to the base. Of course, it could be that the face is perpendicular to the base, but I think the picture should be redrawn. -- Jitse Niesen (talk) 11:12, 20 March 2007 (UTC)
I think one of the definitions is wrong - a parallelepiped isn't a prism, because the translation from each face to the parallel one isn't perpendicular to itself. -Donald Ian Rankin
[edit] Pronunciation
The recent tweaking of the pronunciation information was partly based on a long discussion on Kwami's talk page. Anyone curious about it all should see here (or if that's archived, this diff). Wareh 18:20, 22 October 2007 (UTC)
[edit] Picture
The picture is still misleading. The three vectors do not define the parallelepiped shown. They should have the same length as the three sides. Otherwise, their scalar triple product does not define the volume of the solid.
Also, please show again angle alpha (between a and h). Thanks, Paolo.dL (talk) 13:11, 16 January 2008 (UTC)
- You're right, thanks. Is it now better? -- Jitse Niesen (talk) 15:28, 16 January 2008 (UTC)
Perfect. I really like this picture. Thanks a lot. Paolo.dL (talk) 23:08, 16 January 2008 (UTC)
[edit] Internal angle
I am not sure that the expression "internal angle" is used properly in the "Volume" section. We mean "minimum plane angle" (from among the two possible ones). Paolo.dL (talk) 15:53, 26 May 2008 (UTC)
