Āryabhaṭa numeration
(Redirected from Sanskrit numerals)
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Āryabhaṭa numeration is an alphasyllabic numeral system based on Sanskrit phonemes. It was introduced in the early 6th century in India by Āryabhaṭa, 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 Script error: No such module "lang". = 1 up to Script error: No such module "lang". = 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; Script error: No such module "lang". = 1000000 and so on.
Aryabhata 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 <templatestyles src="Fraction/styles.css" />1⁄5, nja is <templatestyles src="Fraction/styles.css" />1⁄10 and jhardam (jha=9; its half) = <templatestyles src="Fraction/styles.css" />4+1⁄2.Template:Explain
Example
| Example: 299,792,458 | ||||
| 100 101 | 102 103 | 104 105 | 106 107 | 108 |
| 58, | 24, | 79, | 99, | 2 |
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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 (105) and so on. (cf. Indian numbering system)
Another example might be Script error: No such module "Lang". Script error: No such module "lang".,[1] Script error: No such module "val".. Note that in this case, 106(ṛ) and 108(ḷ) parts are swapped, and 106(ṛ) part is ligature.Template:Why
Another example from Aryabhatiya is a verse for table of sines.[2]
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makhi bhakhi phakhi dhakhi ṇakhi ñakhi
ṅakhi hasjha skaki kiṣga śghakhi kighva
ghlaki kigra hakya dhaki kica sga jhaśa
ṅva kla pta pha cha kala-ardha-jyāḥ
Script error: No such module "Check for unknown parameters".
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 10x) values, but these are valid throughout the list of numeric syllables.[3]
| The 33 × 9 = 297 Sanskrit alphabetic numerical syllables | |||||||||||||
| Nine vowels or syllabics | -Script error: No such module "lang". | -Script error: No such module "lang". | -Script error: No such module "lang". | -Script error: No such module "lang". | -Script error: No such module "lang". | -Script error: No such module "lang". | -Script error: No such module "lang". | -Script error: No such module "lang". | -Script error: No such module "lang". | ||||
| अ | इ | उ | ऋ | ऌ | ए | ऐ | ओ | औ | |||||
| × | 10 0 | 10 2 | 10 4 | 10 6 | 10 8 | 1010 | 1012 | 1014 | 1016 | ||||
| Five velar plosives | |||||||||||||
| Script error: No such module "lang". - | क | 1 | क or का Script error: No such module "lang". |
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| Five palatal plosives | |||||||||||||
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| Script error: No such module "lang". - | छ | 7 | छ Script error: No such module "lang". |
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| Five retroflex plosives | |||||||||||||
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| Five dental plosives | |||||||||||||
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| Script error: No such module "lang". - | न | 20 | न Script error: No such module "lang". |
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| Five labial plosives | |||||||||||||
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| Script error: No such module "lang". - | फ | 22 | फ Script error: No such module "lang". |
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| Script error: No such module "lang". - | ब | 23 | ब Script error: No such module "lang". |
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| Script error: No such module "lang". - | भ | 24 | भ Script error: No such module "lang". |
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| Script error: No such module "lang". - | म | 25 | म Script error: No such module "lang". |
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| Four approximants or trill | |||||||||||||
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| Script error: No such module "lang". - | र | 40 | र Script error: No such module "lang". |
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| Script error: No such module "lang". - | ल | 50 | ल Script error: No such module "lang". |
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| Script error: No such module "lang". - | व | 60 | व Script error: No such module "lang". |
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| Three coronal fricatives | |||||||||||||
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| Script error: No such module "lang". - | ष | 80 | ष Script error: No such module "lang". |
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| Script error: No such module "lang". - | स | 90 | स Script error: No such module "lang". |
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| One glottal fricative | |||||||||||||
| Script error: No such module "lang". - | ह | 100 | ह Script error: No such module "lang". |
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See also
References
<templatestyles src="Reflist/styles.css" />
Script error: No such module "Check for unknown parameters".
- Kurt Elfering: Die Mathematik des Aryabhata I. Text, Übersetzung aus dem Sanskrit und Kommentar. Wilhelm Fink Verlag, München, 1975, Template:ISBN
- Georges Ifrah: The Universal History of Numbers. From Prehistory to the Invention of the Computer. John Wiley & Sons, New York, 2000, Template:ISBN.
- B. L. van der Waerden: Erwachende Wissenschaft. Ägyptische, babylonische und griechische Mathematik. Birkhäuser-Verlag, Basel Stuttgart, 1966, Template:ISBN
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