Polygon Names

Date: 09/18/2001 at 12:44:01
From: Judy Davidson
Subject: Polygon terms

Why is a 3-sided polygon called a triangle instead of a tri-gon? 
Why is a 4-sided polygon called a quadrilateral instead of a tetragon, 
when all the others are ___-gons? 
Why is there not a single consistent term?

Date: 09/18/2001 at 13:53:02
From: Doctor Peterson
Subject: Re: Polygon terms

Hi, Judy.

I'd say this is just one of those situations where the small cases (3 
and 4 sides) were named ad hoc, without planning for a consistent 
system, and later new words were added following more of a pattern. 
This happens all the time in English.

"Triangle" uses the Latin "angle" (angulus) rather than the Greek 
"gon" which means the same thing, so it's just the Latin equivalent of 
the Greek "trigon." "Quadrilateral" is even more distinctive, since it 
not only comes from Latin but means "four sides" rather than "four 
angles"; and in fact we DO use the word "quadrangle" sometimes (and 
also "trilateral"). If we were consistent, we would have "trigon" and 
"tetragon" for 3 and 4 sides, using Greek rather than Latin. But 
probably Greek was not so popular when names like triangle and 
quadrilateral moved into English; and of course the most basic answer 
is simply that these words were invented by different people at 
different times, not by an official committee.

According to Merriam-Webster, "triangle" originated in the 14th 
century and "quadrangle" in the 15th (both considered Middle English); 
"polygon" entered the language in 1571, along with "pentagon," 
"hexagon," and many others - clearly as part of a deliberately coined 
set. "Trigon" is listed at 1563, perhaps as a forerunner of those. 
"Quadrilateral" dates from 1650; this makes it somewhat anomalous, and 
I can't explain why it took over from "quadrangle." (We get many 
questions from England that do use the latter term.) 

Jeff Miller's site

   Earliest Known Uses of Some of the Words of Mathematics
   http://members.aol.com/jeff570/mathword.html   

says that

    QUADRILATERAL appears in English in 1650 in Thomas Rudd's
    translation of Euclid. 

Miller also has this (and a lot more) on "polygon":

    POLYGON was used in classical Greek. Euclid, however, preferred 
    "polypleuron," designating many sides rather than many vertices. 

    Polygon appears in English in 1570 in Sir Henry Billingsley's
    translation of Euclid, folio 125. In an addition after Euclid
    IV.16, which Billingsley ascribes to Flussates (Francois de Foix,
    Bishop of Aire), he mentions "Poligonon figures;" and in a
    marginal note explains "A Poligonon figure is a figure consisting
    of many sides." [Ken Pledger] 

This suggests that the use of both "angle" and "side" terms dates all 
the way back to Euclid. Perhaps "quadrilateral" was used as a literal 
translation via Latin; somehow it managed to get into general use, 
unlike "trigon."

English is always interesting!

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/