"tridant" vs. "trident"

[Ben Kovitz <bkovitz -at- IGS -dot- COM>]

The client on a project I'm working on uses an unusual jargon term:
"tridant", meaning a third of a certain geographical area (for which they
have yet another special jargon term).

I recently found out, though, that they think it's spelled "trident".  Their
basis for this is the fact that "tridant" is not in any ordinary dictionary,
but "trident" is.

It seems to me, though, that the correct spelling is definitely "tridant".
 The "trident" they found in the dictionary is not a geographical area, but
a weapon.  It gets the name "trident", of course, from Latin roots for
"three" and "tooth".  A real trident is essentially a spear with three
prongs.  The word "tridant", though not in the dictionary, derives from a
way in Latin for making words for fractions, which is also the basis of the
words "octant", "sextant", and "quadrant".  (The navigation tool "sextant"
was so named because the scale in which it measured angles spanned 60
degrees--a sixth of a circle.)

So I think spelling the word for this geographical division "trident" makes
as much sense as writing "their are seven requirements" or "the
organizational restructuring brought about many unexpected affects."  It
seems unprofessional to misspell it just because the client misspells it.

I don't want to tick off the client, of course, and if they really want it
that way, I'll do it that way.  But I'm wondering if anyone has any other
thoughts.

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