Talk:Parallelepiped

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)

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)

Also, in the first paragraph, I think it should be "...all four definitions (i.e., parallelopiped, parallelogram, cuboid, and rectangle)." As currently, it might imply that Euclidian geometry allows for parallelopipeds to include [regular] cubes and squares, but not oblong cuboids or rectangles. Etymographer (talk) 02:43, 1 July 2020 (UTC)

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)

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

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)

The glottal stop in the archaic British pronunciation is wrong. The cited authorities do not have a glottal stop, and there isn't one in any natural (as apposed to emphatic) British English pronunciation of the old version. (It so happens that one of my colleagues has investigated carefully the phonetics of "unnatural" syllable divisions like el'epiped, and the distinction between (for example) "Norma Nelson" and "Norman Elson" is perceptible with better than chance reliability, but not categorically. The acoustic cues are subtle differences in loudness contours, not a glottal stop.) So I'm removing it, and restoring the pronunciation to what the OED gives. JCBradfield (talk) 10:12, 3 April 2009 (UTC)

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)

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)

The definition of parallelepiped is incorrect. —Preceding unsigned comment added by 85.243.223.112 (talk) 15:24, 7 May 2010 (UTC)

Special cases by symmetry

@Officer781: please, watch math typography. It is ugly when only half of a, b, c are Italic whereas others are Roman, withing few inches of the same article. Variables should be Italic (and preferably serif to avoid the “a” misery), images included. Some uniform style should be chosen for symbols of groups; currently Italic in the table and Roman on the image – jarring. Incnis Mrsi (talk) 15:26, 29 April 2019 (UTC)

I have removed the non-italic markers in the image to make the image more about symmetry as well. Changed the symbols in the table from italic to Roman, while changing the edge parameters from Roman to math mockup to uniformize with image.--Officer781 (talk) 00:42, 30 April 2019 (UTC)