Polygon Names II

Date: 12/11/2003 at 17:06:31
From: Laura
Subject: Polygon Names

For extra credit, my geometry teacher asked us to find out why the 
triangle is named "triANGLE", unlike all the other polygons, which
have names like "quadriLATERAL" or "pentaGON".  But I can't find any
information about it.

Date: 12/12/2003 at 11:47:28
From: Doctor Peterson
Subject: Re: Polygon Names

Hi, Laura.

Words don't always have good reasons behind them; but here are my 
ideas about it (which I found by searching our site for "triangle 
polygon name"):

  Polygon Names
    http://mathforum.org/library/drmath/view/57848.html 

There I suggest that the words "triangle" and "quadrilateral" were 
taken from Latin, while the others were taken from Greek at a 
different time when Greek was more popular. I've just done a little
more research, and find that they actually all came from Latin, which
pushes the question back a little. 

In Latin, as in English, there were both "native" Latin words and
words borrowed from Greek:

  English        Greek         Latin borrowed   Latin native
  -------        -----         --------------   ------------
  triangle       trigonon      trigonum        *triangulum
  quadrangle     tetragonon    tetragonum       quadrangulum
  quadrilateral  tetrapleuron                  *quadrilaterum
  pentagon       pentagonon   *pentagonum       quinquangulum

So when English started to be used in writing about mathematics, the 
Latin terms were borrowed; and presumably some of the preferred Latin 
terms were native Latin words (triangulum and quadrilaterum), and 
some were the Greek (pentagonium). 

So the same argument I made about English applies to the Latin: most
likely the more common objects were usually called by their native
Latin names, while the names for the objects most often discussed by
scholars were taken from Greek, the language in which mathematics was
written at the time.

It's interesting that the Greek tetragonon usually meant "square", 
not just anything with four sides; that may be why the Latin 
"quadrilateral" is used instead of "tetragon" or "quadrangle" in 
English. Since Latin had not borrowed the Greek "tetrapleuron" that 
Euclid would have used, when Euclid was translated to English they 
would have used the native Latin "quadrilateral".

If you have any further questions, feel free to write back.

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