"Subject: [HM] Indian numbers
During my recent visit to India, I learned that when
writing about large numbers, say in newspaper reports on
the budget, they don't use "million", but rather two other
numbers: Lakh, which is a hundred thousand, and Crore,
which is a hundred lakhs. Does anybody know the history of
these units?
Avinoam Mann"
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Dear Dr. Mann,
I am not a member of the HM group but your query was
forwarded to me by my colleague, Prof Paul Ernest. I can
illuminate a little on the use of lakh and crore in Indian
enumeration.
The origins of lakh and crore can be traced to ancient
sanskrit texts. Essentially there were 18 'places' of
numbers or units of reckoning beginning with 1 and
continuing with multiples of 10 until 10^17.
Each unit had a name: 1 = eka, 10 = dasan, 100= sata, 1000
= sahashra, 10000= ayuta, 100000= NIYUTA, 1000000= prayuta,
10000000= KOTI, .....
Aryabahata classed the 18 units into two groups according
to whether they were squares (varga) or non-squares
(avarga). As can be seen from the list the squares are in
the odd places (oja-sthana) while the non-squares are in
the even places (yugma-sthana). [Source: J F Fleet,
'Aryabhata's System of Expressing Numbers' in D.
Chattopadhyaya (ed), "Studies in the History of Science in
India", Asha Jyoti, Delhi, 1992]
For reasons I do not fully understand the use of the 'even'
units 10, 1000, 100000, 10000000 became prevalent for
reckoning in India. In Bhasakara's works NIYUTA (100000)
became laksa (modern lakh). KOTI in modern hindi is crore -
I do not know the exact etymology.
Interestingly, in the ancient sanskrit text, the Ramayana,
the units of reckoning Rama's huge army appear to be lakh,
and a geometric progression with first term crore and
common ratio 1 lakh.
[Source: C N Srinivasiengar, 'The History of Ancient Indian
Mathematics', World Press, Calcutta, 1967]
I hope this is of some help. Feel free to share these
thoughts with others in the HM group.
Dennis Almeida,
The Aryabhata Group,
School of Education,
University of Exeter,
Heavitree Road,
Exeter EX1 2LU.