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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

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.

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)!

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