Talk:Parallelepiped

From Wikipedia, the free encyclopedia

You have new messages (last change).

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)
Retrieved from "http://en.wikipedia.org../../../p/a/r/Talk%7EParallelepiped_0fc2.html"