Parallelepiped.

Scrolling through my Facebook feed this morning (a chore I generally perform once a day), I found a series of posts from He Who Comments Here as under the heading “New students”; the relevant excerpts:

Today I used the word “parallelepiped” in class. I love good old geometry words. (I think that the phrase “good old geometry word” is one of those things I say a little too often when I’m teaching.) […]

By the way, at the blackboard I was clueless as to what the vowel between “parallel” and “piped” was — and I’m usually quite a good speller.

Also, I started wondering where the last part of that word came from. I was going to try to remember to look it up when I got home. No need: there was already an email from another student in the class who had already looked it up. This is one of the little gang who had me assigned as their first-year advisor. I knew he was a collector of arcane geographical knowledge, like myself, but I didn’t know that this applied to etymology, too.

It turns out that “epiped” means something like “plane surface”. Also, in the good old days this good old geometry word was pronounced “parallel-EP-iped”, whereas now we generally say “parallel-a-PIPE-ed”.

I had entirely forgotten the existence of this word, which I probably last heard in high school geometry class, and I too would have been clueless as to what the vowel between “parallel” and “piped” was; I am delighted with the etymology and accepting of the development of pronunciation away from the absurd-unless-you-know-Greek “parallel-EP-iped” to the more sensible “parallel-a-PIPE-ed” (though some people say “parallel-a-PIP-ed”). The OED (entry updated June 2005) has:

Pronunciation: Brit. /ˌparəlɛlᵻˈpʌɪpɛd/ , /ˌparəlɛlᵻˈpɪpɛd/ , U.S. /ˈˌpɛrəˌlɛləˈpaɪpᵻd/ , /ˈˌpɛrəˌlɛləˈpɪpᵻd/
[…]
Etymology: < post-classical Latin parallelepipedum (4th–5th cent.; also 5th–6th cent. in Boethius) or its etymon Hellenistic Greek παραλληλεπίπεδον parallelepipedon n. Compare French parallélépipède (1639; also parallelipipède (1762; attested earlier in Middle French as adjective (1570)). Compare earlier parallelepipedon n.
N.E.D. (1904) gives the pronunciation as (pærălelˌe·piped) /ˌpærəlɛlˈɛpɪpɛd/.

Oh, and if you were wondering, it’s “A solid figure whose faces are six parallelograms, of which opposite pairs are parallel; a prism whose base is a parallelogram.”

Comments

  1. If I wasn’t already familiar with the word “parallelepiped”, I might think it meant “having 3.14159… feet, all of which are parallel”!

  2. I met this word for the first time learning technical Russian. When I began my studies at Warsaw Polytechnic in 1978, Russian was still the obligatory foreign language for all students. As future electronics engineers, we had to absorb a lot of technical and mathematical terminology, and the amazing параллелепипед has remained impressed in my memory ever since.

  3. We’ve kept “parallelepipedum” in ‘Danish’. Wondering whether my pronunciation is correct (-PIP-), I turned to the ODS.

    It isn’t in. But “box” is with the following definition: rectangular, orthogonal parallelepipedum.

    http://ordnet.dk/ods/ordbog?query=Kasse (all the way down at 3.9 (mathematical) – but still …)

  4. I myself say /ˈpærəlɛləˈpaɪˈpɛd/, with multiple primary stresses.

  5. I’m a “parallel-a-PIP-ed” person myself, although I don’t think I’ve heard the word spoken for at least 50 years. Perhaps I’ve never heard it spoken and just invented that myself, for all I know.

    But does this Greek “epiped” include the Greek prefix “epi-” which means something like “beside” in English? Originally I parsed it as “by the foot” but “ped” is Latin not Greek.

  6. Paul Clapham says:

    (Sorry… that last comment was by me but I didn’t spell my name correctly.)

  7. It’s ἐπί upon + πέδον the ground.

  8. It’s been a long time since I’ve seen the word, and longer still since I’ve said it, but my remembered pronunciation is “paraLLELapiped,” with a short ‘i’ for the ‘pip.’ I’ve no idea how I got this but I will blame some forgotten math teacher from long ago.

  9. “ped” is Latin not Greek.

    It’s actually both; the Greek for “foot” is pous, stem pod-, but the same root appears as ped– in other derivatives in Greek.

    (Surely “a series of posts from Him Who Comments Here…”?)

  10. That’s one of those weird intersections of English grammar where no solution sounds right, but “he who” sounds less wrong to my ears than “him who.”

  11. Besides, since I capitalized it I can claim that He Who Comments Here as ∅ is a proper name and thus can’t be altered.

  12. He is part of a name here, so it doesn’t inflect.

  13. I was startled by the “He”, but realized that I would have been startled almost as much by “Him”. Above all I was startled and flattered that an utterance of mine had given rise to a LH post.

    By the way, that same student who went and looked up the etymology before I did also told me that he thought I had pronounced it in class with “piped” pronounced as one syllable — like the past tense of “pipe”! No way. Maybe I should work on speaking more clearly.

  14. J. W. Brewer says:

    Perhaps “Him Wot Comments Here” would be the more elegant solution, although possibility unavailable in AmEng? The “PIPE” version sounds right to me, although it seems likely I have neither heard nor said the word since my teens.

    I suspect none of my Greek professors in college had strong enough math/science backgrounds to peeve about “wrong” pronunciations (here I guess we really mean spelling pronunciations by those to whom the etymology of a given word was opaque) of math/science technical terms of ultimate Greek origin. Maybe one brief discussion of how it was unfortunate that “hyper-” and “hypo-” were essentially homophonous in AmEng casual speech.

  15. Apparently J. K. Rowling is on Hat and JC’s side — Harry eventually defeats He Who Must Not Be Named, not Him Who… I agree that neither option sounds particularly good, which is why I prefer Him Who on logical grounds.

  16. TR, the subject was addressed on A Roguish Chrestomathy in 2007

  17. marie-lucie says:

    He who comments here, He who must not be named

    Compare with She who must be obeyed, which does not inflect either.

  18. I suspect I am one of the few who first encountered this word during my first read through Andrei Belyi’s Peterburg. Perhaps high school geometry ain’t what it used to be.

  19. Взвился бывший алкоголик, матерщинник и крамольник,
    Говорит: “Надо выпить треугольник. На троих его, даешь! ”
    Разошелся, так и сыплет: “Треугольник будет выпит.
    Будь он параллелепипед, будь он круг, едрена вошь! ”

    For the sake of those who didn’t attend Warsaw Polytechnic in 1978, very rough and unartful translation
    Bolted former alcoholic, foul-mouthed rabble-rouser
    Said, “We must drink the [Bermuda] triangle. Let’s split it for the three”
    He got excited and is spitting, “The triangle will be drunk
    Even if it is a parallelepiped, even a circle, fuckin shit!”

  20. For those who don’t know, that’s Vysotsky.

  21. (Note that in that performance he doesn’t actually sing the words “едрена вошь,” just glares meaningfully.)

  22. “The sum of the squares on the twelve edges of any parallelepiped is equal to the sum of the squares on its four diagonals.”

  23. As geometric objects, I rarely if ever have any reason to think about parallelepipeds. However, since I teach various physics courses involving vector algebra and vector calculus, I end up talking about them relatively often. The volume of a parallelepiped provides the geometric interpretation of a vector triple product or (equivalently) a 3×3 determinant.

  24. The volume of any parallelotope is the absolute value of the determinant created from the n row vectors emanating from a vertex.

  25. Sorry, I meant “determinant of the matrix created …”

  26. On the occasion of this post, I looked around for a particular exercise on parallelepipeds I remember from one of Altshiller-Court’s books that I worked through way back when (didn’t find it). It’s odd that I never learned to think of determinants in this way.

  27. I am impressed that the blog software automatically changed the x I typed between the two numerals in my comment into a multiplication sign.

  28. But remember what happened to Mickey Mouse as The Sorceror’s Apprentice, when he got taken in by a piece of intelligent software disguised as a broom. Once it gets going, you can’t stop it.

  29. des von bladet says:

    The geometric view of determinants is emphasised in modern treatments of exterior algebra. In my undergraduate days (late 80s redbrick English university) we still said parallelEPiped, although we knew no Greek.

  30. Well, that pronunciation certainly makes it impossible to forget the spelling. I’m considering whether to adopt it with that goal (mentally, since I’ll probably never have the occasion to use it in conversation); I say “sacri-LEE-jus” for the same reason.

  31. des von bladet says:

    The one that really chafed my scrote was the spelling ‘collinear’. Still not reconciled to that.

  32. Colinear sounds like the co- of linear though, like colimit or cohomology.

  33. I use the word from time to time and pronounce it like the first US pronunciation in OED. It also took me a lot of practice to remember the central vowel in question. Also took me a fair bit of time to learn to resist writing ‘frustrum’ instead of ‘frustum’ (a term which, unlike parallelepiped, honestly doesn’t get used much any more in math).

  34. des: the spelling ‘collinear’. Still not reconciled to that.
    minus273: Colinear sounds like the co- of linear though, like colimit or cohomology.

    Good objection, minus273. Isn’t “col-” just a “con-” where the “n” has got sucked into the following consonant ? (Technical term to follow …). We have collection, collimation, correction, …

    The “co-” in “colimit” is of course etymologically related, but productive in a different, very specific way in mathematics.

  35. We have some idea of how “parallelepiped” was pronounced by one famous writer on determinants, Charles Lutwidge Dodgson, aka Lewis Carroll. From near the end of Sad Souvenaunce, the last canto of Phantasmagoria:

    The hues of life are dull and gray,
    The sweets of life insipid,
    When thou, my charmer, art away—
    Old Brick, or rather, let me say,
    Old Parallelepiped!

  36. Excellent find! So even in Victorian times, not everyone said -EP-iped.

  37. absurd-unless-you-know-Greek “parallel-EP-iped”

    If you know Greek, it’s all the more absurd, since Euclid said παραλληλ-επίπεδον (accenting the antepenult). This is a far as accent can possibly be retracted in Ancient Greek, so the -EP- thing should be unthinkable. Lewis Carroll, who certainly knew Greek, just followed the classical model with his -PIP-. I use a similar pronunciation myself (I can’t remember why) on those extremely rare occasions when the subject of solid geometry is raised in my presence and the language of the conversation is English. I was quite surprised when I looked the word up in John Wells’s Longman Pronunciation Dictionary to find out that the only pronunciations recommended there were /ˌpærəleləˈpaɪped/ and /ˌpærəlelˈepɪped/.

  38. But stress in English has literally nothing to do with (pitch) accent in Greek, which is routinely ignored in the traditional method of teaching Greek (in fact, I have an old textbook that doesn’t even print the accents!). English stress is (traditionally) based on syllable length, i.e. basically the Latin system. Since the i in -pip- is short, the stress is (traditionally) retracted to the previous syllable. The unanglicized form parallelepipedon is pronounced with stress on -pip- for the same reason: the e of -ped- is short, so the stress is retracted to the antepenult (as far back as it can get).

  39. I only wanted to point out that the knowledge of Greek doesn’t justify the -EP- variant (whetever else might). Come to think of it, the reason why I use -PIP- may be the fact that I learnt the word first via Russian as параллелепи́пед — see Vysotsky’s beautiful rhyme: выпит / параллелепипед. In Polish, we use the calque równoległościan.

  40. I only wanted to point out that the knowledge of Greek doesn’t justify the -EP- variant (whetever else might).

    Fair enough; I guess I was using shorthand for “the knowledge of the Greco-Latin element of the English vocabulary and how it historically worked.”

  41. English truly adopted a weird custom to pronounce Latin words without endings, not with the accent on the syllable stressed in Latin, but treating the endingless Latin word as if Latin, and recalculate the stress position with the Latin rules. (sorry for the bad phrasing)

  42. There is actually one rule for Latinate verbs and suffixless adjectives, and a slightly different one for Latinate nouns and adjectives with suffixes. In the former group, you stress the last syllable if it is heavy (but you ignore word-final consonants in calculating syllable weight), and otherwise you stress the penult; in the latter group, you apply the Latin rule, ignoring the last syllable and stressing the penult if heavy, otherwise the antepenult. But since there are lots of special cases, exceptions and variable stress patterns, these rules offer only a rough indication where to place the main stress.

  43. Yes, it is indeed weird and complicated.

  44. My occasion for mentioning the word in my class last week was in fact to give a geometric interpretation of the determinant of a 3 by 3 matrix. I this week when I briefly mention n by n determinants I will also blow their young minds by mentioning n-dimensional parallelotopes.

  45. David Marjanović says:

    in fact, I have an old textbook that doesn’t even print the accents!

    Speaking of blowing young minds…

  46. C. S. Lewis was taught Greek without accents and considered himself ill served for basically the rest of his life.

  47. Alon Lischinsky says:

    I was going to say that the Spanish equivalent paralelepípedo is far more frequent, but apparently Google Ngrams disagrees with me.

    I’m quite surprised; I distinctly recall learning the term when doing geometry in elementary school.

  48. I doubt it’s particularly frequent in any language; geometry class is its natural home.

  49. Lewis Carroll was a *pip*-stresser: in Phantasmagoria (1869), he rhymes parallelepiped rather effectively with insipid.

  50. @Stu (Saturday 11:16am): 12 and 6, surely?

  51. Stu’s right. These are the body diagonals, each one running from the vertex where three of the six faces meet, to the vertex where the other three faces meet. Eight vertices, so four body diagonals.

  52. @rosie Right — and quite trivial in vector notation.

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