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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.
324:(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.)
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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
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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
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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
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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,
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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 cubes and squares, but not oblong cuboids or rectangles.
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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
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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.
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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.
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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,
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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....
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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
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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.
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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).
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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,
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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
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are Italic whereas others are Roman, withing few inches of the same article. Variables should be Italic (and preferably serif to avoid the “
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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. --
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i'm even less confident about this somewhat common-sense terminoology being kosher (even tho i consider it unambiguous), and
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however, would say a cube is just a specialized case of a parallelepiped, and that a face can be square. Who agrees?
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of a face that includes it, and the length of the parallelepiped's altitude relative to that face.
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on
Knowledge. If you would like to participate, please visit the project page, where you can join
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Knowledge. If you would like to participate, please visit the project page, where you can join
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of a parallelepiped is the product of the length of any edge, the length of the corresponding
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I'm feeling a bit cautious (overcautious, probably) about having it visualized perfectly,
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edges and the angles of the parallelograms is probably also worth mentioning. --
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their scalar triple product does not define the volume of the solid
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This is partially copied, and reformatted, from a contrib by
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while i think we need to start with a method that does
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529:Perfect. I really like this picture. Thanks a lot.
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514:You're right, thanks. Is it now better? --
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