Calculus (was Re: Gymnosophists etc.)

[thayashi at doshisha.ac.jp]

At  6:34 PM 96.5.9 +0100, Girish Beeharry wrote:

>Earlier I mentioned the existence of a general article on Indic mathematics 
>which might interest people here. I thought it might be too 'non-Indological'
>for posting here but, now that Professor Deshpande has given a reference to a 
>maths book, I've lost my scrupules...

More too non-Indological information on the Maadhava-Gregory-Leibniz
series, etc.:
%----------------------------
Gold, D. & D. Pingree [1991] `A Hitherto Unknown Sanskrit Work concerning 
M\=adhava's Derivation of the Power Series for Sine and Cosine', {\em
Historia Scientiarum} 42, 49--65.

Gupta, R.C. [1973] `The M\=adhava-Gregory Series' {\em The Mathematics
Education} 7, 3, B, 67--70.

..... [1975] `M\=adhava's and Other Medieval Indian Values of Pi', {\em The
Mathematics Education} 9, 3, B, 45--48.

..... [1976] `M\=adhava's Power Series Computaion of the Sine', {\em
Ga\d{n}ita} 27, 19--24. 

..... [1992] `On the Remainder Term in the M\=adhava-Leibniz's Series', 
{\em Ga\d{n}ita Bh\=arat\=\i} 14, 68--71. 


Hayashi, T., T. Kusuba, M. Yano [1990] `The Correction of the M\=adhava
Series for the Circumference of a Circle', {\em Centaurus}
33, 149--174.

Kususba, T. & T.Hayashi [1993] `Indo ni okeru S\=uretsu' (in Japanese,
Mathematical Series in India', {\em Kagakusi Kenkyu} 185, 32--42.


Marar, K.M. & C.T. Rajagopal [1944] `On the Hindu Quadrature of the
Circle', {\em Journal of the Bombay Branch of the Royal Asistic Society},
NS 20, 65--82.



.... [1981/82] `Power Series in Medieval Indian Trigonometry', {\em
Proceedings of the South Asia Seminar} II (University of Pennsylvania), pp.
25--30.


Rajagopal,C.T. [1949] `A Neglected Chapter of Hindu Mathematics', {\em
Scripta Mathematica} 15, 201--209.


Rajagopal, C.T. & T.V.V. Aiyar [1951] `On the Hindu Proof of Gregory's
Series', {\em Scripta Mathematica} 17, 65--74.


..... [1952] `A Hindu Approximation to Pi', {\em Scripta Mathematica} 18,
25--30.


Rajagopal, C.T. & M.S.Rangachari [1978] `On an Untapped Source of Medieval
Keralese Mathematics', {\em Archive for History of Exact Sciences}
18,
89--102.


..... [1986] `On Medieval Kerala
Mathematics', {\em Archive for the History
of Exact Sciences} 35, 91--99.


Sarasvati Amma, T.A. [1979] {\em Geometry in Ancient & MedievalIndia}. 
Delhi: Motilal.


Saraswathi, T.A. [1963] `The Development of Mathematical Series in India
after Bh\=askara II', {\em Bulletin of the National Institute of Science in
India} 21, 320--343.


Whish, C. M. [1835] `On the Hindu Quadrature of the Circle, and the
infinite Series of the proportion of the circumference to the diameter
exhibited in the four \'{S}\=astras, the Tantra Sangraham, YuctiBh\=ash\=a,
Carana Paddhati, and Sadratnam\=ala', {\em Transactions of the Royal
Asiatic Society of Great Britain and Ireland} 3, 509--523.
%----------------------------
Hayashi