Origin Of Numerals

THE ORIGIN OF NUMERALS Today's numbers, also called Hindu-Arabic numbers, are a combination of just 10 symbols or digits: 1, 2, 3, 4, 5, 6, 7, 8, 9, and 0. These digits were introduced in Europe within the XII century by Leonardo Pisano (aka Fibonacci), an Italian mathematician. L. Pisano was educated in North Africa, where he learned and later carried to Italy the now popular Hindu-Arabic numerals. Hindu numeral system is a pure place-value system, that is why you need a zero. Only the Hindus, within the context of Indo-European civilisations, have consistently used a zero. The Arabs, however, played an essential part in the dissemination of this numeral system. Numerals, a time travel from India to Europe The discovery of zero and the place-value system were inventions unique to the Indian civilization. As the Brahmi notation of the first 9 whole numbers... However, the first Western use of the digits, without the zero, was reported in the Vth century by Beothius, a Roman writer. Beothius explains, in one of his geometry books, how to operate the abacus using marked small cones instead of pebbles. Those cones, upon each of which was drawn the symbol of one of the nine Hindu-Arabic digits, were called apices. Thus, the early representations of digits in Europe were called “apices”. Each apex received also an individual name: Iginfor 1, Andras for 2, Ormis for 3, Arbas for 4, Quimas (or Quisnas) for 5 , Caltis (or Calctis) for 6, Zenis (or Tenis) for 7, Temenisa for 8, and Celentis (or Scelentis) for 9. The etymology of these names remains unclear, though some of them were clearly Arab numbers. The Hindu-Arabic-like figures reported by Beothius were reproduced almost everywhere with the greatest fantasy! (see below) Before adopting the Hindu-Arabic numeral system, people used theRoman figures instead, which actually are a legacy of the Etruscan period. The Roman numeration is based on a biquinary (5) system. To write numbers the Romans used an additive system: V + I + I = VII(7) or C + X + X + I (121), and also a substractive system: IX (Ibefore X = 9), XCIV (X before C = 90 and I before V = 4, 90 + 4 = 94). Latin numerals were used for reckoning until late XVI century! The graphical origin of the Roman numbers ©1992-2011, Sarcone & Waeber
		Other original systems of numeration
Other original systems of numeration were being used in the past. The "Notae Elegantissimae" shown below allow to write numbers from 1 to 9999. They are useful as a mnemotechnic aid, e.g. the symbol K in the example may mean 1414 (the first 4 figures of the square root of 2).
		Chinese and Japanese contributions
The Ba-Gua trigrams (pron. pah-kwah, 八卦) and the Genji-Kopatterns (源氏香), antique Chinese  and Japanese symbols, are strangely enough related to mathematics and electronics. If all the entire lines of the trigrams (___) are replaced with the digit 1 and the broken lines (_ _) with the digit 0, each Ba Gua trigram will then represent a binary number from 0 to 7. You can also notice that each number is laid in front of its complementary: 0<>7, 1<>6, 2<>5, etc. Write "a", "b", "c", "d" and "e" under the five small red sticks of each Genji-Ko pattern. By doing so, you will have the 52 manners to CONNECT 5 variables in boolean algebraics. The linked sticks form a "conjunction" (AND, .), and the isolated sticks or groups of sticks form a "disjunction" (OR, +). The pattern at the top left represents: [("a" and "d") or ("b" and "e") or "c"]   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).   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 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 (fromdwidekomt) 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 (fromhunda-rada: 'the number 100') cent hundrede ehun 1000 mille thousand (fromthus-hundi: 'swollen hundred') mille tusind mila Indo-European languages Non Indo-European languages Numbers in some synthetic languages... Esperanto Volapük Interlingua 12 3 4 5 6 7 8 9 10 11 12 13 20 21 22 30 40 50 90 100 1000 unudu tri kvar kvin ses sep ok nau dek dekunu dekdu dektri dudek dudekunu dudekdu tridek kvardek kvindek naudek cento mil baltel kil pol lul mäl vel jöl zül bals balsebal balsetel balsekil tels telsebal telsetel kils pols luls züls tum balstum unduo tres quattro cinque sex septe octo novem dece undece duodece tredece vinti vinti-un vinti-duo trenta quaranta cinquanta novanta cento mille