Definitions

ordinal-numeral

Indian numerals

Most of the positional base 10 numeral systems in the world have originated from India, which first developed the concept of positional numerology. The Indian numeral system is commonly referred to in the West as Indian (Hindu-Arabic) numeral system, since it reached Europe through the Arabs.

Devanagari numerals and their Sanskrit names

Below is a list of the Indian numerals in their Devanagari form, the corresponding European (Indo-Arabic) equivalents, and their Sanskrit pronunciation.

Devanagari
numeral
Indian/Hindu Sanskrit word for
the ordinal numeral (wordstem)
0 (शून्य)
1 (एक)
2 (द्वि)
3 (त्रि)
4 (चतुर्)
5 (पञ्च)
6 (षष्)
7 (सप्त)
8 (अष्ट)
9 (नव)

Since Sanskrit is an Indo-European language, it is obvious (as also seen from the table) that the words for numerals closely resemble those of Greek and Latin. The word "Shunya" for zero was borrowed into Arabic as "sifr", which became the term "zero" in many European languages from Medieval Latin, zephirum (Arabic: sifr).

Other modern Indian languages

The four Indian languages (Hindi, Marathi, Konkani and Sanskrit itself) that have adapted the Devanagari script to their use also naturally employ the numeral symbols above; of course, the names for the numbers vary by language. The table below presents a listing of the symbols used in various modern Indian scripts for the numbers from zero to nine:

Variant 0 1 2 3 4 5 6 7 8 9 Used in
Eastern Nagari numerals Bengali language
Assamese language
Gujarati numerals Gujarati language
Gurumukhi numerals Punjabi language
Kannada numerals Kannada language
Malayalam numerals Malayalam language
Tamil numerals ௦0 Tamil language
Telugu numerals Telugu language
Lepcha numerals | Sikkim and Bhutan

Note: The symbols for zero in Tamil and Malayalam are modern innovations. Unicode 4.1 and later define encodings for them.

History

A decimal place system has been traced back to ca. 500 in India. Before that epoch, the Brahmi numeral system was in use; that system did not encompass the concept of the place-value of numbers. Instead, Brahmi numerals included additional symbols for the tens, as well as separate symbols for hundred and thousand.

The Indian place-system numerals spread to neighboring Persia, where they were picked up by the conquering Arabs. In 662, a Nestorian bishop living in what is now called Iraq said:

I will omit all discussion of the science of the Indians ... of their subtle discoveries in astronomy - discoveries that are more ingenious than those of the Greeks and the Babylonians - and of their valuable methods of calculation which surpass description. I wish only to say that this computation is done by means of nine signs. If those who believe that because they speak Greek they have arrived at the limits of science would read the Indian texts they would be convinced even if a little late in the day that there are others who know something of value.

The addition of zero as a tenth positional digit is documented from the 7th century by Brahmagupta, though the earlier Bakhshali Manuscript, written sometime before the 5th century, also included zero.

As it was from the Arabs that the Europeans learned this system, the Europeans called them Arabic numerals; ironically, to this day the Arabs refer to their numerals as Indian numerals. In academic circles they are called the Hindu-Arabic or Indo-Arabic numerals.

The significance of the development of the positional number system is probably best described by the French mathematician Pierre Simon Laplace (1749 - 1827) who wrote:

It is India that gave us the ingenious method of expressing all numbers by the means of ten symbols, each symbol receiving a value of position, as well as an absolute value; a profound and important idea which appears so simple to us now that we ignore its true merit, but its very simplicity, the great ease which it has lent to all computations, puts our arithmetic in the first rank of useful inventions, and we shall appreciate the grandeur of this achievement when we remember that it escaped the genius of Archimedes and Apollonius, two of the greatest minds produced by antiquity.

Tobias Dantzig, the father of George Dantzig had this to say in Number:

This long period of nearly five thousand years saw the rise and fall of many a civilization, each leaving behind it a heritage of literature, art, philosophy, and religion. But what was the net achievement in the field of reckoning, the earliest art practiced by man? An inflexible numeration so crude as to make progress well nigh impossible, and a calculating device so limited in scope that even elementary calculations called for the services of an expert [...] Man used these devices for thousands of years without contributing a single important idea to the system [...] Even when compared with the slow growth of ideas during the dark ages, the history of reckoning presents a peculiar picture of desolate stagnation. When viewed in this light, the achievements of the unknown Hindu, who some time in the first centuries of our era discovered the principle of position, assumes the importance of a world event.

References

See also

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