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Topic: 12 sided figure
Replies: 3   Last Post: Dec 20, 2003 9:45 AM

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John Conway

Posts: 2,238
Registered: 12/3/04
Re: 12 sided figure
Posted: Dec 18, 2003 12:29 PM
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On 17 Dec 2003, Jeffrey Cai wrote:

> My teacher told me it was an undecagon.I agree with it because of the
> word "undecillion."

However, this is a misleading analogy. The words "billion",
"trillion","quadrillion", "quintillion", ... introduced by
Chuquet and de la Roche are based on Latin, while the terms
"pentagon", "hexagon", "heptagon", ... were originally Greek.

Many lexicographers take the view that their job is just to
record existing usages, and so you can indeed find the macaronic
forms "septagon", "nonagon", "undecagon" in various dictionaries.
But when asked "what are the correct names for these polygons?"
one should obviously give the all-Greek forms "heptagon",
"enneagon", "hendecagon".

However, I wish it were possible to stop mathematics teachers from
asking these questions! The answers are not important, and they're
certainly not part of mathematics, in which the term "17-gon" is
surely preferable to the official "heptakaidecagon". If they do
insist on asking them, though, they should at least learn the correct
answers. Nobody says "quintagon", and nobody should say "septagon"
or "undecagon".

Let me tell those who ARE interested in the "official" names, that
Antreas Hatzipolakis and I once worked out a complete system of
Greek-derived "English" prefixes for all numbers below 100,000. Up to
100 it reads:

mono hendeca icosikaihena
di dodeca icosikaidi
tri triskaideca icosikaitri
tetra tetrakaideca icosikaitetra
penta pentakaideca icosikaipenta
hexa hexakaideca icosikaihexa
hepta heptakaideca icosikaihepta
octa octakaideca icosikaiocta
ennea enneakaideca icosikaiennea
deca icosa triaconta tetraconta ... enneaconta hecta.

Some comments are in order.

1) the structure is easy to remember because it mirrors the
English names for numbers, in that we have special words for 1-12
followed by the "N-kaideca" words in analogy to "N-teen" and then
the "icosikai-N" words analogous to "twenty-N", etc.

2) One sometimes meets the shorter forms obtained by omitting "kai"
(which means "and"). The "kai" forms are more correct, and only
they permit the extension to strings of numbers that is used, for
instance, in Kepler's "icosidodecahedron".

3) In these English forms, the final vowels (except those in
mono, di, tri) have been uniformised to "a", although in the original
Greek one had, for instance "octo" and "penteconta".

4) The form for "one" is really "hena" rather than "mono", which
really means something like "single". So it would be silly to use
(say) "icosi(kai)monogon" for "21-gon".

5) The proper Greek term for a 100-gon would be something like
"hecatontogon" rather than our "hectagon". But the shortened prefix
"hecta-" for "100" is already well-established in the international
scientific vocabulary.

John Conway

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