| From: "John Conway" <[email protected]>
Subject: Re: 11-gon
Date: Mon, 24 Oct 94 20:10:39 EDT
I have obviously missed an interesting discussion on 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
______________________________________________
From: "John Conway" <[email protected]>
Subject: Re: 11-gon
Date: Mon, 24 Oct 94 21:16:16 EDT
I see someone asked about the 24-gon, 48-gon, 96-gon. The
"official" names are
icositetragon
tetracontaoctagon
enneacontahexagon
if anyone cares. A "myriagon" would be a polygon with 10000 sides.
The word "macaronic" is usually used for a word made of pieces
from several languages - one doesn't need "linguistic heteromorph"!
John Conway
______________________________________________
From: "John Conway" <[email protected]>
Subject: Re: 11-gon
Date: Mon, 24 Oct 94 21:21:28 EDT
By the way, "icositetrahedron" appears in some dictionaries.
The dual of the rhombicuboctahedron has been called either
a trapezoidal or tetragonal icositetrahedron, while the dual
of the snub cube is a pentagonal icositetrahedron.
I saw the word "tetrakaidecahedron" in a recent "press release"
from the Minneapolis Geometry Center, so you can see that people
DO occasionally use such words.
John Conway
______________________________________________
From: "John Conway" <[email protected]>
Subject: Re: 11-gon
Date: Mon, 24 Oct 94 21:35:08 EDT
I'm working my way back through all this email. I see that
"undecagon" and "duodecagon" have been rearing their ugly
heads again. The full set is
monogon, digon, trigon, tetragon, pentagon, hexagon, heptagon, octagon
(of which monogon and digon can only be used in rather special circumstances;
it's digon not "bigon"; and trigon and tetragon are alternatives to "triangle"
and "quadrilateral" - the adjectival forms "trigonal" and "tetragonal"
being more common), then
enneagon, decagon, hendecagon, dodecagon, triskaidecagon, tetrakaidecagon,...
not
nonagon undecagon duodecagon
but tridecagon and tetradecagon (&c)
are OK.
The (synonymous) words "triskaidecaphobia" and "tridecaphobia"
appear in dictionaries (occasionally spelled with a "k" instead
of that "c"). I was reminded of them in O'Hare airport yesterday,
as I passed gates 10,11,12,14,15,... !
John Conway
______________________________________________
Craig Roberts Dec. 6, 1994
Geometry - Period Three
Dover-Sherborn High School
[email protected]
Below is my first attempt to name the polygons with 3 sides up to 50 sides.
I made this attempt after reading the recent conversation on
geometry.pre.college.
Feedback is welcome. ([email protected])
NAMES OF THE POLYGONS
3 TRIANGLE
4 QUADRILATERAL
5 PENTAGON
6 HEXAGON
7 SEPTAGON
8 OCTAGON
9 ENNEAGON
10 DECAGON
11 HENDECAGON
12 DODECAGON
13 TRIDECAGON
14 QUADECAGON
15 PENDECAGON
16 HEXDECAGON
17 SEPTDECAGON
18 OCTDECAGON
19 ENNEADECAGON
20 ICOSAGON
21 ICOSITEMONOGON
22 ICOSITEDIGON
23 ICOSITETRIGON
24 ICOSITETRAGON
25 ICOSITEPENTAGON
26 ICOSITEHEXAGON
27 ICOSITESEPTAGON
28 ICOSITEOCTAGON
29 ICOSITENONAGON
30 TRIACONTAGON
31 TRICONTAMONAGON
32 TRICONTADIGON
33 TRICONTATRIGON
34 TRICONTATETRAGON
35 TRICONTAPENTAGON
36 TRICONTAHEXAGON
37 TRICONTASEPTAGON
38 TRICONTAOCTAGON
39 TRICONTAENNEAGON
40 TETRACONTAGON
41 TETRACONTAMONOGON
42 TETRACONTADIGON
43 TETRACONTATRIAGON
44 TETRACONTATETRAGON
45 TETRACONTAPENTAGON
46 TETRACONTAHEXAGON
47 TETRACONTASEPTAGON
48 TETRACONTAOCTAGON
49 TETRACONTAENNEAGON
50 PENTACONTAGON
_______________________________________
There is an "official" set of names for polygons, uniformly derived
from the Greek after 4 sides, and you have some of them wrong.
"septa" is Latin, not Greek - the official version is "hepta"
The typical twenty-something is (eg) "icositetra"
and the typical thirty-something is (eg) "tricontapenta"
(which would also tell you what the typical forty-something would be.)
JHConway
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