Āryabhaṭa numeration is an
alphasyllabic numeral system based on
Sanskrit phonemes. It was introduced in the early 6th century in India by
Āryabhaṭa
Aryabhata ( ISO: ) or Aryabhata I (476–550 CE) was the first of the major mathematician-astronomers from the classical age of Indian mathematics and Indian astronomy. His works include the '' Āryabhaṭīya'' (which mentions that in 3600 ' ...
, in the first chapter titled ''Gītika Padam'' of his ''
Aryabhatiya''. It attributes a numerical value to each syllable of the form consonant+vowel possible in
Sanskrit phonology, from ' = 1 up to ' =
1018.
History
The basis of this number system is mentioned in the second stanza of the first chapter of ''
Aryabhatiya''.
The Varga (Group/Class) letters ''ka'' to ''ma'' are to be placed in the varga (square) places (1st, 100th, 10000th, etc.) and Avarga letters like ''ya'', ''ra'', ''la'' .. have to be placed in Avarga places (10th, 1000th, 100000th, etc.).
The Varga letters ''ka'' to ''ma'' have values from 1, 2, 3 .. up to 25 and Avarga letters ''ya'' to ''ha'' have values 30, 40, 50 .. up to 100. In the Varga and Avarga letters, beyond the ninth vowel (place), new symbols can be used.
The values for vowels are as follows: ''a'' = 1; ''i'' = 100; ''u'' = 10000; ' = 1000000 and so on.
Aryabhata
Aryabhata ( ISO: ) or Aryabhata I (476–550 CE) was the first of the major mathematician-astronomers from the classical age of Indian mathematics and Indian astronomy. His works include the '' Āryabhaṭīya'' (which mentions that in 3600 ' ...
used this number system for representing both small and large numbers in his mathematical and astronomical calculations.
This system can even be used to represent fractions and mixed fractions. For example, ''nga'' is , ''nja'' is and ''jhardam'' (''jha''=9; its half) = .
Example
The traditional Indian digit order is reversed compared to the modern way. By consequence, Āryabhaṭa began with the ones before the tens; then the hundreds and the thousands; then the
myriad and the
lakh
A lakh (; abbreviated L; sometimes written lac) is a unit in the Indian numbering system equal to one hundred thousand (100,000; scientific notation: 105). In the Indian 2, 2, 3 convention of digit grouping, it is written as 1,00,000. F ...
(10
5) and so on. ''(cf.
Indian numbering system
The Indian numbering system is used in India, Pakistan, Nepal, Sri Lanka, and Bangladesh to express large numbers, which differs from the International System of Units. Commonly used quantities include ''lakh'' (one hundred thousand) and ''crore' ...
)''
Another example might be ', . Note that in this case, 10
6(ṛ) and 10
8(ḷ) parts are swapped, and 10
6(ṛ) part is ligature.
Another example from
Aryabhatiya is a verse for
table of sines.
[
]
Numeral table
In citing the values of Āryabhaṭa numbers, the short vowels अ, इ, उ, ऋ, ऌ, ए, and ओ are invariably used. However, the Āryabhaṭa system did not distinguish between long and short vowels. This table only cites the full slate of क-derived (1 x 10
x) values, but these are valid throughout the list of numeric syllables.
See also
*
Aksharapalli
*
Bhutasamkhya system
*
Katapayadi system
*
IAST
The International Alphabet of Sanskrit Transliteration (IAST) is a transliteration scheme that allows the lossless romanisation of Brahmic family, Indic scripts as employed by Sanskrit and related Indic languages. It is based on a scheme that ...
References
* Kurt Elfering: ''Die Mathematik des Aryabhata I. Text, Übersetzung aus dem Sanskrit und Kommentar''. Wilhelm Fink Verlag, München, 1975,
* Georges Ifrah: ''The Universal History of Numbers. From Prehistory to the Invention of the Computer''. John Wiley & Sons, New York, 2000, .
* B. L. van der Waerden: ''Erwachende Wissenschaft. Ägyptische, babylonische und griechische Mathematik''. Birkhäuser-Verlag, Basel Stuttgart, 1966,
*
*
{{DEFAULTSORT:Aryabhata Numeration
Numerals
Classical ciphers
Indian mathematics