Talk:Parallelepiped

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[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)

[edit] Picture

Vectors and volume of a parallelepiped

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)

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