A few details can be found in:
Histoire des Sciences Arabes, Roshdi Rashed editor
(Editions du Seuil, 1997)
The book is written in French, and I do not know if it was ever translated.
This article is by B. Rosenfeld and P. Youschkevitch, and I quote the
main ideas:
The method seems to be rather classical (similar to Archimedes'):
a_n is the side, and b_n the chord such that a_n, b_n, 2R is a right
triangle. The algorithm is, in modern notations,
b_2n = sqrt [ R * (2R + b_n )]
Starting with an equilateral triangle, Al-Kashi performs 28 iterations,
and this value is said to be chosen because, if D = 2R was 600,000 times
the diameter of the Earth (the supposed size of the universe, at that
time), the difference between the length of circle and polygon would be
less than a horsehair.
Another source is :
J.P. Delahaye, "Le Fascinant Nombre Pi" (Belin-Pour la Science)
It doesn't have more information, but you can join the author at
delahaye@lifl.fr
Maybe he knows something else about this story...
Best regards,
**************************************
Alain JUHEL
lycee Faidherbe, LILLE
Tel : 03.20.77.63.69
e-mail : ajuhel@nordnet.fr
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