Prof. R. Sridharan, CMI, India
Mathematics

While it was an easy matter for the Greeks to construct the mean proportion of two segments, using straight edge and compass, the question of finding two mean proportionals between two segments, a question to which the Delian problem of duplication of the cube which had been reduced by Hippocrates, turned out to be unsolvable if one allowed oneself only these instruments. Archytas of Taras (430 B.C - 365 B.C) a brilliant colleague of Plato (though not belonging to the Platonic tradition) found an ingenious method of solving this problem, using special and kinematic techniques. We briefly talk about this method and some related questions. We also discuss in this connection the contributions of his student Eudoxus, a many sided genius and that of Manaechmus (a brilliant student of Eudoxus).

Roughly contemporaneous with Archytas, there lived in India the illustrious Pingala, who was a Sanskrit prosodist, who initiated by his work the genesis of combinatorics in India. This enumerative combinatorics has had a continued history, evolved with many ramifications (for instance, the Fibonacci numbers were discovered in India centuries before Fibonacci during this evolution). We note that the remarkable work of Sarangadeva ( 13th century A.D, "Sangita ratnakara") deals with the enumeration of the n! permutations of n symbols (for n=7) and the associated unique representation of integers in terms of factorials.