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Topic: Names of polygons
Replies: 26   Last Post: Apr 29, 2008 12:08 PM

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John Conway

Posts: 2,238
Registered: 12/3/04
Re: 11-gon
Posted: Oct 24, 1994 4:10 PM
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I have obviously missed an interesting discussion of names for polygons!

Anyway, I'll throw in what I know, since such things have always interested
me.

1) For the "numerical" part of the name, one should use the Greek
prefixes:

mono, di, tri, tetra, penta, hexa, hepta, octa, ennea,

deca, hendeca, dodeca, trideca, etc, icosa, triaconta, hecta ..

10 11 12 13 20 30 100

A 24-gon would thus officially be an icositetragon.

There are variations in spelling and formation

(eg dekagon, endecagon, triskaidecagon,...)

(the "kai" here means "and")

The "gon" has an interesting etymology : it is ultimately
derived from the Greek word "gonu" for "knee", which they
transferred to "angle".

This word goes straight back to the Indo-European, and is
essentially the same in lots of languages:

gonu (greek)
genu (latin)
k nee (english)

French is similar to Latin here, and German to English (except
that the "K" is still pronounced.

3) The "hedron" in "polyhedron" is also an Indo-European
word, meaning "seat". A "cathedral" church is one that contains
a seat from which a bishop hands down authoritative opinions
(cata = down, hedron = seat).

In accordance with Grimm's law, the "h" is Greek
correesponds to "s" in English, while "d" may soften to "t"
and "p" or "b" to "f" or "v". So look:

penta
five hexa
six hepta
seven hedr
seat ped
foot

4) In summary, a "polygon" is a thing with many knees,
and a "polyhedron" a thing with many seats.

I mentioned "ped" because it happens in that curious
word "parallelepiped", which should really be pronounced
parallel-epi-ped. Until about the middle of the 19th century
this word was even longer - "parallelepipedon". It splits
into parts thus

para - allele - epi - ped - on

beside other upon ground

(memo - "pedon", meaning the ground, is what you put your foot on)

Two things are "parallel" if one is beside the other - this was
already used as a single word very early on. What the name
means is that there's always a face that's parallel to the one
upon the ground.

The term "allele" in modern biological use, is one of the
"alternatives" that goes in a certain place along a chromosome.

5) The word "trapezium" has an interesting history. A
Greek word for "table" was "tetrapedon" or "tetrapes", meaning
"four legs". This then was used for "table-shaped", meaning
quadrilateral. The particular kind of quadrilateral has changed
around a bit over the years. Originally, it was used only for
rectangles, but later for arbitrary quadrilaterals, and it is only
quite recently that is has been specialized to those with two
parallel sides. So in some scientific uses, "trapezoidal"
refers to things with arbitrary quadrilateral faces, not just
to those whose faces are trapeziums in the modern sense.

By the way, of course the circus "trapeze" is just a
trapezium, in the sense of "rectangle".

I hope that someone else out there finds this nearly as
interesting as I do.

John Conway






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