Aryabhata numeration
The Āryabhaṭa numeration is a system of numerals 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 ka = 1 up to hau = 1018.
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 kak to ma have value from 1, 2, 3 .. up to 25 and Avarga letters ya to ha have value 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; ṛ = 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 1/5, nja is 1/10 and Jhardam (jha=9; its half) = 4½.
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)
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