> One of my students asked about the standardization of terminology for
> polygons. Specifically, he asked what the name for a forty-one sided
> polygon was in English and who had decided on that. A reference would be
> appreciated (paper or electronic) and a response could be offnet in case the
> subject has already been discussed at length. Thank you.
Well, of course there hasn't actually been an international
conference at which standard names were drawn up and agreed upon!
What's happened instead is just that the traditional Greek names
have become the de facto standards in most European languages.
Since these names uniformly consist of a number-prefix followed
by the affix "-gon" (meaning "angle"), it's fairly clear how
the system continues more or less indefinitely, except that there
are some slight variations.
Let me explain a few of the latter. One thing is that the Greek
names for numbers have changed slightly over the years, so that 14
has been called both "tetradeka" and "tetrakaideka" (the latter
meaning "4 and 10"). Another is that "deca" is so spelled in most
of the English words in which it appears, rather than "deka", which
is the more obvious transliteration. A third is that although the
Greek prefixes tend to alter as they form compounds (so for instance
"penta" becomes "pente" in "penteconta" = 50), this is less natural
in English. Finally, I'll note that "octagon" is the established
English spelling for what would be "octogon" if taken directly from the
Greek.
Some years ago, with lots of help from Antreas Hatzipolakis and
a bit more help from some other Greek speakers, I worked out a
regular system going up to a million. The prefixes in this system are:
mono,di,tri,tetra,penta,hexa,hepta,octa,ennea,deca,hendeca,dodeca,
triskaideca,tetrakaideca,pentakaideca,...,enneakaideca, icosa,
icosikaihena,icosikaidi,icosikaitri,...,icosikaiennea, triaconta,
triacontakaihena,triacontakaidi,... , tetraconta,...,pentaconta, ... .
As you'll see, we chose the "kai" forms for numbers from 13
onwards (for very good reasons), and regularized things so that
most of the prefixes end in "a". It's nice that the number-prefixes
of this system behave like the English number-names, in that we
have special names for 1-12, then prefixes ending in "deca" for
numbers whose English names end in "teen", followed by ones
starting with "icosi" where the English starts with "twenty", and
so on. In this system
"tetracontakaihenagon"
is the name for a 41-sided polygon.
But let me say that we did this mostly for fun, and that I personally
would call it a "41-gon"!
John Conway