Query: unknown quantities

[Artur Karp]

At 10:16 20.09.98 -0400, you wrote:
>My twelve year old son brought home a math assignment on Friday that
>involves "ancient Hindu" mathematics. I have not been able to help him, as
>my knowledge of this field is limited, as are the resources available at
>home.
>
>The question is: What notation did ancient Greek and ancient Hindu
>mathematicians use for unknown quantities? I have taken this to refer to
>such unknown quantities as we might indicate by x, y, and z, or other
>letters in such expressions as 2x = 4.
>
>The Encyclopedia Britannica article "History of Mathematics" mentions
>Diophantus of Alexandria (lived some time between 2nd century BC and 3rd
>century AD) as having used a figure resembling the Roman letter S as the
>unknown quantity, but does not mention if Indian mathematicians used any
>such figures. Secondary sources at home that treat Indian mathematics in
>any way do not treat this matter. Rapid and superficial perusal of the few
>Sanskrit mathematical texts I have suggests to me that there may be no
>figurative or symbolic notation, but I would welcome any informed answer,
>so that I can help my son answer his question.
>
>Thank you in advance.
>
>
>Elliot M. Stern
>552 South 48th Street
>Philadelphia, PA 19143-2029
>USA
>
>telephone: 215 747 6204
>
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S.N. Sen in "A Concise History of Science in India" [Chapter "Mathematics";
New Delhi 1971; pp. 189-200] writes on the matter:

"... Various terms for the unknown quantity are met with in the Hindu
mathematical literature, e.g. yavat-tavat, yadrccha, vanccha, varna,
kamika, gulika and avyakta.

...For the equations the various technical terms used were sama-karana,
sami-karana, sadrsi-karana, etc. The Sthananga-sutra classifies them
according to the powers of unknown quantity into the following: the simple
(yavat-tavat), the quadratic (varga), the cubic (ghana) and the biquadratic
(varga-varga)...

...For writing algebraic equations it is necessary to use some kind of
symbols for the unknown quantities, symbols of operations, powers and
roots. For unknown quantities we have noticed the practice of using a
symbol for zero or vacant place in the Bakhshali MS. The use of the letters
of the alphabet is strongly indicated by the use of the word varna (letters
of the alphabet). Various colour names, e.g. kalaka (black), nilaka (blue),
pita (yellow), lohita (red), or abbreviations of the names of precious
gems, e.g. ma (for manikya, ruby), ni (for indra-nila, sapphire), mu (for
mukta-phala, pearl), etc., served this purpose..."

Hoping it helps,

Artur Karp

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