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### Polygon Names

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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
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://jeff560.tripod.com/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/
```
Associated Topics:
Elementary Definitions
Elementary Geometry
Elementary Triangles and Other Polygons
Middle School Definitions
Middle School Geometry
Middle School Triangles and Other Polygons

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