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Numbers' & Numeral systems' history and curiosities

 
Origins of the Numerals
Page 1 / Page 2 / More...

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...

hindu-arabic numerals

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: Igin for 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)


hindu-arabic numerals

Before adopting the Hindu-Arabic numeral system, people used the Roman 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 (I before 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
roman number historic

roman symbols
©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).

nota elegantissima

 

    Chinese and Japanese
contributions
   

The Ba-Gua trigrams (pron. pah-kwah, 八卦) and the Genji-Kô patterns (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.

bagua
The "Genji-Kô" (源氏香) symbols used for the chapters of the Tale of Genji (early Japanese novel) indicate the possible groupings and subgroupings of 5 elements. For instance, if you write down "a", "b", "c", "d" and "e" beneath the five small red sticks of each Genji-Kô pattern, you will obtain 52 distinct ways to connect 5 variables in Boolean algebra. 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"]

genji koh
©1992-2011, Sarcone&Waeber, all rights reserved

 
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