|
|
|
| |
Shortcuts |
| |
 |
 |
|
 |
Numbers' & Numeral
systems' history and curiosities (2)
|
|
| A
journey through the past |
Page
1 / Page 2 / More...
|
|
|
|
How
did the Mayas represent numbers?
The
Mayas, as well as the Aztecs, used a vigesimal (20) numeration.
They developed 3 sets of different graphical notations
to represent numbers: a) with strokes and dots, b) anthropomorphic
figures, c) symbols.
|
a) The
Mayan base-20 numeral system
b) The
figures shown below indicate numbers from 0 to 10
|
| |
|
Chinese
Numbers |
|
|
|
The
Peculiarity of the Chinese Numeral Notation
The
Chinese use three numeral systems: the Hindu-Arabic
numerals, along with two indigenous numeral systems,
one for everyday writing (simple numerals), and another
one for use in commercial or financial contexts (complex
numerals). These last ones are used on checks and other
transaction forms because they are much more difficult
to alter. Actually, they are the equivalent of writing
'one', 'two', 'three', etc., rather than 1, 2, 3...
In
the chart below, the first column features European or
Hindu-Arabic numerals; the second one, the standard Chinese
equivalent (simple numerals); and the third column, the "capital" Chinese
characters (complex numerals).
|
The
Chineses also had several other ways to represent numbers.
The strange geometric figures shown below indicate the
numbers 1 through 10. This numeration style - named shang
fang da zhuan - is still used in official seals.
|
©1997-2011,
Sarcone & Waeber
|
| |
|
Early
Egyptian Fractions |
|
|
|
'Horus
eye' or udjat was
used to transcribe unit measures of capacity for grains,
as you can see below each part of the eye represents
a value in binary unit fraction (fig. 1). The Egyptians
were also the inventors of the
fraction bar. The numerator 1 and the bar were represented
by a graphical symbol suggesting an open mouth; they
used to note the denominators of the fraction under
this symbol (fig. 2).  More
info about Egyptian fractions here.
Did
you know that the Romans too could transcribe unit fractions?
E.g. to record 1/2
they used the letter S (semis). Knowing that,
what represents SIX? Obviously
not 6, but 8.5 (=10-1-0.5)!
|
©1997-2011,
Sarcone & Waeber
|
| |
|
The
Origin of the Numbers' Names |
|
|
Numbers
1 through 10 in Various Writing Systems
(More
numerals in many different writing systems from Omniglot)
Indo-European
Heritage
The
number names in most European languages take their origin
from the Indo-European language. Although various numeration
systems have been used (duodecimal, vigesimal and sexagesimal
numerations), the decimal system survived all of them.
However, we can find traces of the vigesimal system in
some French, Danish and Basque number names.
|
Numbers
in some early European languages
|
Languages
using a decimal system |
using
a vigesimal system |
| Indo-European |
Sanskrit |
Etruscan |
Latin |
Gaulish (old
celt) |
| 1 |
oin-
(-os, -a, -om), sem- |
eka
(-ah, -a, -am) |
thu |
unus,
-a, -um |
un |
| 2 |
dwo(u)
m., dwoi f., n. |
dva
(dvau, dve, dve) |
zal,
(e)sal |
duo,
-ae, o |
duo |
| 3 |
treyes
m., tisores f., tri n. |
tri
(trayah, trini, tisras) |
ci |
tres,
tria n. |
tri |
| 4 |
kwetwores,
kwetesres f. |
(e)catur
(eka+tri?) |
sà |
quattuor
(quattuora n.) |
petuor |
| 5 |
penkwe |
panca
(orig. "fist"?) |
mach |
quinque |
pinp,
pemp |
| 6 |
seks,
sweks |
sas |
huth |
sex |
suex |
| 7 |
septem |
sapta |
semph
(?) |
septem |
sextan |
| 8 |
okto |
asta |
cezp
(?) |
octo |
oxtu |
| 9 |
newn |
nava
(orig. "1 left..."?) |
nurph-
(?) |
novem |
naun |
| 10 |
dekem |
dasa
(orig. "2 hands"?) |
sar,
zar |
decem |
decan |
| 17 |
septemdekem |
saptadasa |
ci-em
zathrum (20-3) |
septemdecim |
septandecan |
| 18 |
oktodekem |
astadasa |
esl-em
zathrum |
duodeviginti
(20 - 2) |
oxtudecan |
| 19 |
newndekem |
unavimsati
(20-1) |
thun-em
zathrum |
undeviginti
(20 - 1) |
naudecan |
| 20 |
wikemti
(from dwidekomt) |
vimsati |
zathrum |
viginti
(>vinti, vulg.) |
ugant |
| 30 |
trikomte
(3x10) |
trimsat |
cialch,
cealch |
triginta |
decan
ugant(ic) (10+20) |
| 40 |
kwetworkomte
(4x10) |
catvarimsat |
sealch |
quadraginta |
duogant(ic)
(?) (2x20) |
| 50 |
penkwekomte
(5x10) |
pancasat |
muvalch |
quinquaginta |
decan
duogant (10+2x20) |
| 60 |
seks-komte
(6x10) |
sasti |
huthalch |
sexaginta |
triugant(ic)
(?) (3x20) |
| 70 |
septemkomte
(7x10) |
saptati |
semphalch |
septuaginta |
decan
triugant (?) (10+3x20) |
| 80 |
oktokomte
(8x10) |
asiti |
cezpalch
(?) |
octoginta |
petorugant(ic)
(?) (4x20) |
| 90 |
newnkomte
(9x10) |
navati |
nurphalch
(?) |
nonaginta |
decan
petorugant (10+4x20) |
| 100 |
kemton |
satam |
|
centum |
cant(on) |
| 1000 |
(smi)gheslom |
dasa
satani, sahasram |
|
mille,
milia (meille, arch.) |
mille |
| 0 |
|
suna |
|
zephyrum
(lat. med.) |
|
Numbers
in some modern European languages
|
Languages
using a decimal system |
using
both decimal + vigesimal |
using
a vigesimal system |
| Italian |
English |
French |
Danish |
Basque |
| 1 |
uno |
one |
un |
een |
bat |
| 2 |
due
(doi) |
two |
deux |
to |
ni |
| 3 |
tre |
three |
trois |
tre |
hiru |
| 4 |
quattro |
four
(from fidwor) |
quatre |
fire |
lau |
| 5 |
cinque |
five
(from fimf) |
cinq |
fem |
bortz |
| 6 |
sei |
six |
six |
seks |
sei |
| 7 |
sette |
seven |
sept |
syv |
zapzi |
| 8 |
otto |
eight |
huit
(orig. vit) |
otte |
zortzi |
| 9 |
nove |
nine |
neuf |
ni |
bederatzi |
| 10 |
dieci |
ten |
dix |
ti |
hamar |
| 11 |
undici |
eleven
(from ainlif: 1 left over) |
onze |
elleve |
hameka |
| 12 |
dodici |
twelve
(twalif: 2 left over) |
douze |
tolv |
hamabi |
| 17 |
diciassette |
seventeen |
dix-sept |
sytten |
hama-zapzi |
| 18 |
diciotto |
eighteen |
dix-huit |
atten |
hama-zortzi |
| 19 |
diciannove |
nineteen |
dix-neuf |
nitten |
hama-bederatzi |
| 20 |
venti |
twenty
(a score) |
vingt |
tyve |
hogoi |
| 30 |
trenta |
thirty |
trente |
tredive |
hogoi
ta hamar (20+10) |
| 40 |
quaranta |
forty |
quarante |
fyrre |
berrogoi
(2x20) |
| 50 |
cinquanta |
fifty |
cinquante |
halvtreds
(2.5 x "20") |
berrogoi
ta hamar (2x20+10) |
| 60 |
sessanta |
sixty |
soixante |
tres
(3 x "20") |
hirur
hogoi (3x20) |
| 70 |
settanta |
seventy |
soixante-dix
(60+10) |
halvfyerds
(3.5 x "20") |
hirur
hogoi ta hamar (...+10) |
| 71 |
settantuno |
seventy
one |
soixante-onze
(60+11) |
enoghalvfyerds |
hirur
hogoi ta hameka (+11) |
| 80 |
ottanta |
eighty |
quatre-vingts
(4x20) |
firs
(4 x "20") |
laurogoi
(4x20) |
| 90 |
novanta |
ninety |
quatre-vingt-dix
(4x20+10) |
halvfems
(4.5 x "20") |
laurogoi
ta hamar (4x20+10) |
| 91 |
novantuno |
ninety
one |
quatre-vingt-onze
(4x20+11) |
enoghalvfems |
aurogoi
ta hameka (...+11) |
| 100 |
cento |
hundred
(from hunda-rada: 'the number 100') |
cent |
hundrede |
ehun |
| 1000 |
mille |
thousand
(from thus-hundi: 'swollen hundred') |
mille |
tusind |
mila |
| Indo-European
languages |
Non
Indo-European languages |
Numbers
in some synthetic languages...
|
Esperanto |
Volapük |
Interlingua |
| 1
2
3
4
5
6
7
8
9
10
11
12
13
20
21
22
30
40
50
90
100
1000 |
unu
du
tri
kvar
kvin
ses
sep
ok
nau
dek
dekunu
dekdu
dektri
dudek
dudekunu
dudekdu
tridek
kvardek
kvindek
naudek
cento
mil |
bal
tel
kil
pol
lul
mäl
vel
jöl
zül
bals
balsebal
balsetel
balsekil
tels
telsebal
telsetel
kils
pols
luls
züls
tum
balstum |
un
duo
tres
quattro
cinque
sex
septe
octo
novem
dece
undece
duodece
tredece
vinti
vinti-un
vinti-duo
trenta
quaranta
cinquanta
novanta
cento
mille |
|
| |
|
To
end, some curiosities |
|
|
Can
you count in Dalmatian, an antique and now extinct italic
language spoken along the Dalmatian coasts (former Yugoslavia)?
Here is how: (1 to 22) join, doi, tra, quatro, cenk, si, sapto, guapto, nù, dik, jonco, dotko, tretko, quatvarco, cionco, setko, dikisapto, dikinù, venc', vencejoin, vencedoi,
...(30, 40, 50, ...100 and 1'000) tranta, quaruanta, cionquanta, sesuanta, septuanta, guaptuanta, nonuanta, ciant, mel...
• Can
you count in DingBong?
Believe
it or not, Machoumearobilengmonoolemongametsoarobilengmonoolemong
means "99" in the language of the Bassoutos
tribe.
 More
number curiosities here!
|
"Numeral
and Numbers' history and curiosites" are excerpts of our
math columns "Alchimaths". You can read them in the review
'Tangente' (French version). To subscribe write to:
Editions Archimède, 5 rue Grandel,
95100 Argenteuil, France |
| You
are encouraged to expand and/or improve this article. Send
your comments, feedback or suggestions to Gianni
A. Sarcone. Thanks! |
We
welcome the re-use and distribution of the content published
on this Web page on the condition that you credit us by including
the following information: "Copyright © 1992-2011,
Gianni A. Sarcone, Archimedes-Lab.org. Used with the permission".
You may not use this editorial content for commercial purposes! |
 |
|
|
 Back
to previous page
 Continue
to Number Encyclopedy
|
|
