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There is a word for a quarter of a circle or a plane: "quadrant".

What is the corresponding word for a third of a circle? "tridrant" or "terdrant" or something different?

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There's no word that I'm aware of that means a third of a circle. We have quadrant (1/4), sextant (1/6) and octant (1/8) but nothing for a third beyond the generic term: a sector.

You could call it a one-third sector or a 120 degree sector.

Based on numerical prefixes, if there was such a word it would be 'tridant' but this isn't a word you'll find in any dictionary and most people would assume you'd misspelled 'trident'.

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    Worth noting however, that "sextant" usually refers to this navigation tool
    – James Webster
    Sep 25, 2015 at 14:29
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    @JamesWebster, I never would have thought about it before, but that tool is so named because it's about one-sixth of a circle!
    – Carl Kevinson
    Sep 25, 2015 at 17:50
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    @CarlKevinson, it is indeed. There are similar tools called octants and quintants named with the same rational. Just those tools aren't as common, hence the reason why I would still relate those terms to geometry instead of navigation.
    – James Webster
    Sep 25, 2015 at 17:55
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    "A tripartite division of something" is standard English, but not quite applicable to the question. (As in the joke schoolboy translation of Caesar's Latin phrase tres partes - "he quartered the whole of Gaul into three halves")
    – alephzero
    Sep 25, 2015 at 19:50
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Trine.

trine

trīn/

Astrology

noun

  1. an aspect of 120° (one third of a circle).

However this is a fairly obscure word, I think.

Edit: upon further inspection it appears this word refers to a group of three, not a single third.

trine (trīn) n.

  1. A group of three.

  2. In astrology, the aspect of two planets when 120° apart.

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  • As "trine" is also present in French for "astronomical description", I suggest this answer should get more upvites.
    – Laurent Duval
    Sep 25, 2015 at 23:46
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    In formal mathematics and science, it is probably not a great idea to use astrology words.
    – Kevin
    Sep 26, 2015 at 0:06
  • @Kevin why not?
    – fonini
    Sep 26, 2015 at 8:44
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    @fonini: because many scientists in your audience hate, are afraid of, or are inordinately frustrated by astrology. The fact that the word is used by astrologers will create guilt by association, which might not be rational but is certainly a thing. Now, I think there are ways to defuse this, and that it's reasonably safe to take a single term, clearly defined in your paper, to use in a context where a word for that concept is needed. But you can imagine what happens if you go too far and start slinging astrology jargon left and right.
    – Steve Jessop
    Sep 26, 2015 at 9:30
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    My area is engineering, not mathematics, but I think the prejudice towards astrology applies as well. My point is: if I wanted to use a word from any other area in my paper, I wouldn't like to be forced to refrain just because some people can't cope with it. And I would be very mad at any editor who told me to do so. And, actually, I really don't think I would get in any kind of trouble for borrowing a word from astrology (if I could motivate it convincingly)
    – fonini
    Sep 26, 2015 at 10:29

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