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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
mayan numerals

b) The figures shown below indicate numbers from 0 to 10
maya numbers

 

    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).

Chinese 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.


old chinese numbers
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). arrow 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)!

egyptian binary fractions
©1997-2011, Sarcone & Waeber

 

    The Origin of the Numbers' Names    

 

Numbers 1 through 10 in Various Writing Systems
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?) 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, , 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.

freccia 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

     
tangente 1 tangente 2 tangente 3

You are encouraged to expand and/or improve this article. Send your comments, feedback or suggestions to Gianni A. Sarcone. Thanks!
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