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Topic: What's the word?
Replies: 11   Last Post: Aug 3, 1999 3:25 PM

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John Conway

Posts: 2,238
Registered: 12/3/04
Re: What's the word?
Posted: Mar 24, 1996 10:08 AM
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On Fri, 22 Mar 1996, Michael Keyton wrote:

>
> Does any one know or have a word for two arcs whose measures sum to 360
> degrees? I seem to recall having read that they are called complementary
> arcs. My students have suggested bi-supplementary or circplementary. As I
> read the etymology, both complementary and supplementary mean virtually
> the same thing "something that completes or fills up". Thus its use in
> complementary sets. Likewise looking for a word for for two angles whose
> sum is 270 degrees? Their contributions have been tricomplementary or
> sesquisupplementary.
>
> Michael Keyton
> St. Mark's School of Texas
> Dallas
>


Quite nice suggestions, but I don't really like the way everything has two
names under this system - for example complementary = semisupplementary
and supplementary = bicomplementary, even though these words have never
been used. Also, they have the disadvantage that the words don't
actually MEAN what we want - for example a "semisupplement" is
etymologically be something that supplies just half of what's needed
to complete it to something (and I'm sure that "the semisupplement of A"
has actually been used for (180 - A)/2 , correctly, in my view. In
a similar way, the "tricomplement of A" should mean 3(90 - A).

In the older usage, angles were called "complementary" if they added
up to ANY multiple of 90 degrees; to be more precise one would say
they were "complements in 270 degrees", say, or equally "complements
to 270 degrees". I haven't looked it up in the OED (I'll do so when I
get back to Princeton), but I suspect that the same is true of
"supplements" too. This is just to use these words in their ordinary
senses and English (or, originally, Latin or French words), namely

a COMPLEMENT is what you have to add to COMPLETE something
("completement"), while

a SUPPLEMENT is something that SUPPLIES what's needed.

("complement" is the older word of the two).

It's a pity that the 90 degree usage of the word complement is
established, since to my mind the most natural "completement" of
a given angle is the one that completes it to a full circle.

I have been toying with words like "remainder", "residue",
but the more common forms of these already have so many technical
uses that they'd be misleading here. Also, it would be nice to
have a term that "rhymes" with the existing two.

The best I've managed to come up with is

REMANENT, which is more or less obsolete as a noun meaning
whatever remains when something is taken away, but still survives
in its adjectival form.

So how about "the remanent angle of A" for 360 degrees - A,
and "mutually remanent angles" for angles that add to 360 degrees?

I really don't think we need any special term for
complements in 270 degrees, but note that if A and B are
complementary, then their supplements do add to 270 degrees,
so "having complementary supplements" is an adjectival phrase
that describes angles adding to 270 degrees.

John Conway







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