NAMES of the n-gons?
John Rickert
>In article <1992Mar6.1...@galois.mit.edu> jb...@riesz.mit.edu (John C. Baez) writes:
>>In article <1992Mar6.0...@msc.cornell.edu> put...@msc.cornell.edu (Albert Putnam) writes:
>>>What are the English (German/French) names of the
>>>first forty n-gons?
[deletions]
>11 undecagon
Do you have a reference for this? It should be hendecagon, as "hendeca"
is the Greek word for "eleven." (Etymology buffs might note that "hen"
shows up in "hyphen.")
>21 unicosagon
Likewise here. "uni-" is Latin but not Greek. Should it be something
like "eikosikaihenagon"? (Sounds a bit much, though.)
>In all cases, the "-ecagon" part may be spelled "-ekagon", with no apparent
>rhyme or reason for the choice.
Sometimes kappa is transliterated "k," other times "c." The first is
more "authentic," e.g., "Sokrates," the second is more traditional,
often coming through Latin, e.g., "Thucydides."
>-'d' Kidd / Eric Idle / ESG / Eric Gindrup
>`````````````````````````````````````````````````````````````````````````````
>`gin...@hardy.math.okstate.edu (preferred) If at first you don't `
>` succeed, deficit spend. It `
>`uucp 'a.cs.okstate.edu!/dev/null' (flames) works for the Federal Gov't.`
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John Rickert One swallow does not make
rick...@athena.cas.vanderbilt.edu a spring, nor a day.
--Aristotle, Ethics
Eric `'d'kidd' G..
>In article <1992Mar6.0...@msc.cornell.edu> put...@msc.cornell.edu (Albert Putnam) writes:
>>What are the English (German/French) names of the
>>first forty n-gons?
>>
>>20-gon dodecagon
>
>Sorry, dodeca- means 12.
>
>
3 trigon (as in trigonal planar...)
4 quadrilateral or quadrangle
5 pentagon
6 hexagon
7 heptagon
8 octagon
9 nonagon
10 decagon
11 undecagon
12 dodecagon (sometimes dua-)
13 triskadecagon (like the phobia) or tridecagon (short i)
14 quadradecagon (apparently chosen to be consistent with 4-gon)
15 pentadecagon
16 hexadecagon (like the number base)
17 heptadecagon (occasionally septadecagon)
18 octadecagon
19 nonadecagon
20 icosagon (don't ask me... I just work here... You want fries with that?)
21 unicosagon
22-29 like 12-19, but (prefix)-icosagon
30-40 I don't remember anymore
In all cases, the "-ecagon" part may be spelled "-ekagon", with no apparent
rhyme or reason for the choice. Also, "-agon" is sometimes spelled "-ogon"
but, again, inconsistently in my experience. (As long as the writer is
consistent, who cares.)
Albert Putnam
I can name a few English ones:
3-gon triangle
4-gon quadrilateral
5-gon pentagon
6-gon hexagon
8-gon octagon
9-gon nonagon
10-gon decagon
20-gon dodecagon
Please include references for obscure ones
i.e those not in the average dictionary.
If you know n-gons for n>40 feel free to send those too.
If you post, please e-mail me as well.
Scharle
|> What are the English (German/French) names of the
|> first fourty n-gons?
|>
|> I can name a few English ones:
|> 3-gon triangle
|> 4-gon quadrilateral
|> 5-gon pentagon
I'm not trying to be facetious, but what about 2-gon and 1-gon?
--
Tom Scharle |cm65n6@irishmvs(Bitnet)
Room G003 Computing Center |sch...@lukasiewicz.cc.nd.edu(Internet)
University of Notre Dame Notre Dame, IN 46556-0539 USA
John C. Baez
>
>I can name a few English ones:
J.K.Pearson
>first fourty n-gons?
>
>I can name a few English ones:
>3-gon triangle
>4-gon quadrilateral
>5-gon pentagon
These don't look like English to me, all Greek except quadrilateral which
is latin for some reason(oh for a classical education).
>Please include references for obscure ones
>i.e those not in the average dictionary.
>If you know n-gons for n>40 feel free to send those too.
>If you post, please e-mail me as well.
Liddell and Scott, Greek Lexicon might make names of them in, but the problem
with Liddell and Scott is you have to know the word before you can find it.
Perhapes you should learn to count in classical greek, for this I recomend
finding a classical greek textbook. Plenty around.
Regards
Justin.
P.S.
Don't ask me what they are, since it is years since I did any Greek.
--
------------------------------------------------------------------------------
Justin Pearson, | So what do you thinks going on? |
University of Kent at Canterbury | |
U.K. | |
Michael Hartley
> I'm not trying to be facetious, but what about 2-gon and 1-gon?
Now, why don't we just let bigons be bigons?
--
+-----------------------------------------------------------------------+
It has been said that the vast majority of educated people believe in
evolution because they have been assured that the vast majority of
educated people believe in evolution...
Gary Martin
sch...@lukasiewicz.cc.nd.edu (Scharle) writes:
> I'm not trying to be facetious, but what about 2-gon and 1-gon?
Now, why don't we just let bigons be bigons?
I've resisted so far, but no longer: Is a 0-gon all gone?
--
Gary A. Martin, Assistant Professor of Mathematics, UMass Dartmouth
Mar...@cis.umassd.edu
David E. Joyce
>In article <1992Mar6.1...@galois.mit.edu> jb...@riesz.mit.edu (John C. Baez) writes:
>>In article <1992Mar6.0...@msc.cornell.edu> put...@msc.cornell.edu (Albert Putnam) writes:
>>>What are the English (German/French) names of the
>>>first forty n-gons?
>
To get an idea what the dictionaries had to say about it, I ripped through
Webster's Third New International Dictionary Unabridged.
I don't think the Webster's third is the authority in these matters, in fact,
looking over the missing entries below, you can see it's not complete. But I
do have a copy and it does have a lot of words. I looked through the expected
entries for 3-20 sided polygons and found these. Some of the expected ones
were missing, and some were there that I've never heard of.
3 triangle, trigon, trilateral
4 quadrangle, quadrilateral, tetragonal (adj. only)
5 pentagon, quinquangle (archaic)
5/2 pentacle, pentagram, pentalpha, pentangle
6 hexagon, sexagonal (adj. only), sexangular (adj. only)
6/2 hexagram
7 heptagon
8 octagon, octangular (adj. only)
9 nonagon
10 decagon
11 undecagon
12 dodecagon
15 pentadecagon
Along with this table, I'd like to see a table for polyhedra (should look
pretty similar), big numbers (million, billion, trillion, ...), and n-tuples
(pairs, triples, quadruples, ...).
I wonder why the 3-gon is usually name triangle, the 4-gon quadrilateral, and
the n-gon (Greek or Latin prefix)gon? Why not all angles, laterals, or gons?
Just before posting this, I decided to check the OED (Oxford English
Dictionary) even though my copy is too small to see. Here's what I found with
a quick search. I probably missed a few.
3 triangle, trigon, trilateral
4 quadrangle, quadrilateral, tetragon
5 pentagon, quinquangle (obs. rare), quinquangular (adj.), pentangle
(rare), pentangular (adj.)
5/2 pentacle, pentagram, pentalpha, pentangle, pentagonon (obs.)
6 hexagon, hexangle (obs.), hexangular (adj.), sexagon, sexangle (obs.)
6/2 hexagram
7 heptagon, septangle (obs.)
8 octagon, octangle (obs.), octangular (adj.)
9 enneagon, nonagon
10 decagon
11 hendecagon, undecagon (incorrect)
12 dodecagon
15 quindecagon, quindecangle (rare)
Just because a word doesn't appear in the OED doesn't mean it hasn't been used
and shouldn't be used.
As for the enneagon/nonagon and hendecagon/undecagon debate, since these words
are so rarely used, I'd recommend following the regular rule, that is Greek
numeric prefix followed by -gon. In fact, it looks like the only exceptions
should be the triangle and quadrilateral, and those only because they're in
common use. (I suppose you could argue that since "triangle" is used more
than all the rest together, it should be used as the paradigm and change all
the rest to a numeric prefix followed by -angle!) Alternatively, for large
n-gons, just replace n by the specific number, for instance, 9-gon.
--
David E. Joyce Dept. Math. & Comp. Sci.
Internet: djo...@black.clarku.edu Clark University
BITnet: djoyce@clarku Worcester, MA 01610-1477
Allan Adler
an example of a four sided triangle. It is a nonconvex quadrilateral,
having three acute angles internally and one internal angle greater
than a straight angle. Apparently, such angles were not regarded as
angles of the figure, so although it had 4 sides, Proclus only counted
it as having 3 angles, i.e. the 3 angles less than a straight angle.
See vol. I of Heath's edition of Euclid's Elements, p.188.
Allan Adler
a...@altdorf.ai.mit.edu
Eric `'d'kidd' G..
>>3 trigon (as in trigonal planar...)
>>4 quadrilateral or quadrangle
>>5 pentagon
>>6 hexagon
>>7 heptagon
>>8 octagon
>>9 nonagon
>>10 decagon
>>11 undecagon
>>12 dodecagon (sometimes dua-)
>>13 triskadecagon (like the phobia) or tridecagon (short i)
>>14 quadradecagon (apparently chosen to be consistent with 4-gon)
>>15 pentadecagon
>>16 hexadecagon (like the number base)
>>17 heptadecagon (occasionally septadecagon)
>>18 octadecagon
>>19 nonadecagon
>>20 icosagon (don't ask me... I just work here... You want fries with that?)
>>21 unicosagon
>>22-29 like 12-19, but (prefix)-icosagon
>>30-40 I don't remember anymore
>
>pretty similar), big numbers (million, billion, trillion, ...), and n-tuples
>(pairs, triples, quadruples, ...).
>
>David E. Joyce Dept. Math. & Comp. Sci.
>Internet: djo...@black.clarku.edu Clark University
>BITnet: djoyce@clarku Worcester, MA 01610-1477
Polyhedra:
4 Tetrahedron
5 (?) Pentahedron
6 Hexahedron
7 Heptahedron
8 Octahedron
(Gee... These prefixes look familiar... ;-)
Big Numbers:
exp American Continental(???? I'm not European...)
3 Thousand Thousand
6 Million Million
9 Billion Milliard
12 Trillion Billion
15 Quadrillion Billiard (???)
18 Quintillion Trillion (??? Here my command of European usage lapses.)
21 Sextillion
24 Septillion
27 Octillion
30 Nonillion
(Again, these prefixes look familiar...)
N-Tuples:
2 Pair, Duple, Duet, Duo
3 Triad, Triple, Trio
4 Quadruple, Quartet
5 Quintuple, Quintet
6 Sextuple , Sextet
7 Heptuple , Heptet (Maybe Sept-)
8 Octuple
(One more time into the breach...)
Well?....
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God is an engineer, and his approximation is no better than Plank's Constant.
Claus Schoenleber
> In article <1992Mar6.0...@msc.cornell.edu>, put...@msc.cornell.edu (A
> |> What are the English (German/French) names of the
> |> first fourty n-gons?
> |>
> |> I can name a few English ones:
> |> 3-gon triangle
> |> 4-gon quadrilateral
> |> 5-gon pentagon
> [...]
> I'm not trying to be facetious, but what about 2-gon and 1-gon?
>
What English try Huh, attention: greek try ;-)
----------------------------------------------------------------------
1-gon point enogon
2-gon segment (of a line) dyogon
infinity-gon circle myriogon
----------------------------------------------------------------------
:-)
Any comments?
Claus.
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Metzstr. 54 |ISBN 3-926986
D-W-2300 Kiel 1, Germany |phone +49 431 18863
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Intelligence is overhead. | "What's the matter?" - "Never mind!"
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SCOTT I CHASE
>----------------------------------------------------------------------
> 1-gon point enogon
> 2-gon segment (of a line) dyogon
>infinity-gon circle myriogon
>----------------------------------------------------------------------
>
Yes.
A Myriogon should have 10,000 sides.
-Scott
P.S. I recently found the word "centuplicate" meaning to multiply by 100
in my dictionary. Cool, huh?
Scharle
...
|>
|> What English try Huh, attention: greek try ;-)
|> ----------------------------------------------------------------------
|> 1-gon point enogon
|> 2-gon segment (of a line) dyogon
|> infinity-gon circle myriogon
|> ----------------------------------------------------------------------
|>
|> :-)
Excuse me, I am not a mathematician, but a 2-gon is a figure with two
line segments, right? So far I have heard "bigon", "digon" and now "dyogon"
(two of them with smileys), and for 1-gon the present "enogon" and for
1-gon on a sphere "hemisphere". No idea of what Greek for "infinite" is.
Michael Hartley
He gives the following
24-hedroid = ikosatetrahedroid
120-hedroid = hekatonikosihedroid
600-hedroid = hexakosioihedroid
Yours, Mike H...
Claus Schoenleber
> In article <6LcFHB...@elrond.toppoint.de>, fre...@elrond.toppoint.de (Cla
> ...
> |>
> |> What English try Huh, attention: greek try ;-)
> |> ----------------------------------------------------------------------
> |> 1-gon point enogon
> |> 2-gon segment (of a line) dyogon
> |> infinity-gon circle myriogon
> |> ----------------------------------------------------------------------
> |>
> |> :-)
> ...
> Excuse me, I am not a mathematician, but a 2-gon is a figure with two
> line segments, right? So far I have heard "bigon", "digon" and now "dyogon"
> (two of them with smileys), and for 1-gon the present "enogon" and for
> 1-gon on a sphere "hemisphere". No idea of what Greek for "infinite" is.
>
I think, I'd say "point" to a 1-gon, "segment" to a 2-gon, because for
n < 3 there are no real "knees" (I think the "-gon" comes from greek for "knee",
or am I wrong?)
The greek word for "infinity" (= uncountable many) is something like
"myrioi" (normally spelled in greek letters); you know it from the
English word "myriad". So I think my "myriogon" might be correct for a circle.
;-)
Regards,
Jim Propp
(Claus Schoenleber) writes:
>sch...@lukasiewicz.cc.nd.edu (Scharle) writes:
>The greek word for "infinity" (= uncountable many) is something like
>"myrioi" (normally spelled in greek letters); you know it from the
>English word "myriad". So I think my "myriogon" might be correct for a circle.
>;-)
In his book "Regular Polytopes", H.S.M. Coxeter calls polygons with
infinitely many sides "apeirogons". However, an apeirogon is not a
circle but a sequence of equal segments of a line.
My other favorite word from this book is "hosohedron".
Jim Propp
Math Department
M.I.T.
mkro...@amherst.edu
> sch...@lukasiewicz.cc.nd.edu (Scharle) writes:
>
>> I'm not trying to be facetious, but what about 2-gon and 1-gon?
>
> Now, why don't we just let bigons be bigons?
In bygone days, a 2-gon was known as a digon.
mkro...@amherst.edu
> In article <1992Mar6.1...@galois.mit.edu> jb...@riesz.mit.edu (John C. Baez) writes:
>>In article <1992Mar6.0...@msc.cornell.edu> put...@msc.cornell.edu (Albert Putnam) writes:
>>>What are the English (German/French) names of the
>>>first forty n-gons?
>>>
> 9 nonagon
AKA enneagon.
Afroditi Michailidi
>
>I think, I'd say "point" to a 1-gon, "segment" to a 2-gon, because for
>n < 3 there are no real "knees" (I think the "-gon" comes from greek for "knee",
>or am I wrong?)
You are :-). 'Knee' in (ancient) Greek is 'gony' -- however all these -gons
do not have an 'omikron' but an 'omega' (you know, that vowel that looks like
'w' :-) and the ending is derived from 'gwnia' meaning 'angle'. So polygon
just means 'many angled', pentagon means 'five angled' etc. I find this
interesting as I normally think of polygons in terms of their _sides_ rather
than their _angles_ but oh well... must be all these Graphics classes :-)
>
>The greek word for "infinity" (= uncountable many) is something like
>"myrioi" (normally spelled in greek letters); you know it from the
>English word "myriad". So I think my "myriogon" might be correct for a circle.
>;-)
Literally, 'myrioi' means 10,000 (well, *almost* an infinity for practical
purposes :-)) as witnessed for example in Xenophon's Anabasis.
The Greek word for infinity, as some other netter has pointed out is 'apeiro'.
Yet another post with no math in it. (Actually I had this question about
how much time on average it will take to match cassette tapes and their boxes
assuming you start with a random box, open it, move its contents to their
rightful place, move those previously occupying that space into _their_
rightful place etc. etc. but my collection isn't that large yet :-)
>
>Regards,
>
>Claus.
Afroditi
*****************************************************
Warning: Graduate student -- overworked and underpaid
*****************************************************
Claus Schoenleber
> In article <iPPkHB...@elrond.toppoint.de> fre...@elrond.toppoint.de (Clau
> [the bigons be bygones etc. discussion]
> >
> >I think, I'd say "point" to a 1-gon, "segment" to a 2-gon, because for
> >n < 3 there are no real "knees" (I think the "-gon" comes from greek for "kn
> >or am I wrong?)
>
> You are :-). 'Knee' in (ancient) Greek is 'gony' -- however all these -gons
> do not have an 'omikron' but an 'omega' (you know, that vowel that looks like
> 'w' :-) and the ending is derived from 'gwnia' meaning 'angle'. So polygon
> just means 'many angled', pentagon means 'five angled' etc. I find this
> interesting as I normally think of polygons in terms of their _sides_ rather
> than their _angles_ but oh well... must be all these Graphics classes :-)
>
For my "knowledge base" is only a small book about ancient greek from where
I got my "knowledge" I have to believe you. :-)
> >
> >The greek word for "infinity" (= uncountable many) is something like
> >"myrioi" (normally spelled in greek letters); you know it from the
> >English word "myriad". So I think my "myriogon" might be correct for a circl
> >;-)
>
> Literally, 'myrioi' means 10,000 (well, *almost* an infinity for practical
> purposes :-)) as witnessed for example in Xenophon's Anabasis.
>
> The Greek word for infinity, as some other netter has pointed out is 'apeir
>
'
_ _ '
Yes, myrioi means 10,000, and myrioi means inumerable (if I got this correct
from that book, but I have to believe you more I think).
Regards,
Claus.
p.s.: back to math :-)