Inspired induction

Several centuries before Newton or Leibniz, a group of mathematicians- now known as the Kerala school- had discovered infinite series, particularly for trigonometric functions. Although they cannot be credited with having invented calculus, they had some knowledge of mathematical induction and had obtained a number of results which they gave without proof.

Many of the mathematicians of this school were known: one of them, Jyeshtadevan's key work was the Yuktibhasa which he wrote in Malayalam. this text is considered unique in the history of Indian mathematics in that it contains proofs of theorems and derivations of rules and series. One major criticism of classical Indian mathematics is that it as largely ignorant of the methods of mathematics...

HBA in New Delhi have just brought out the Ganita-Yukti-Bhàshà of Jyeshtadeva (Rationals in Mathematical Astronomy). The Malyalam text has been critically edited and translated by K V Sarma, with explanatory notes by K Ramasubramanian, M D Srinivas and M S Sriram in two volumes, Mathematics and Astronomy. Running to 1084 pages, this two volume hardcover set is priced at Rs. 1500.00.

"The text comprising fifteen chapters is naturally divided into two parts, Mathematics and Astronomy, and purports to give an exposition of the techniques and theories employed in the computation of planetary motions as set forth in the great treatise Tantrasaïgraha (c.1500).

The Mathematics part is divided into seven chapters and the topics covered are Parikarma (logistics), fractions, rule of three, Kuññàkàra (linear indeterminate equations), Paridhi and Vyàsa (infinite series and approximations for the ratio of the circumference and diameter of a circle) and Jyànayana (infinite series and approximations for sines). A distinguishing feature of the work is that it presents detailed demonstrations of the famous results attributed to Màdhava (c.1340-1420), such as the infinite series for, the arc-tangent and the sine functions, the estimation of correction terms and their use in the generation of faster convergent series. Demonstrations are also presented for some of the classical results of Āâryabhaña (c.499) on Kuññàkàra or the process of solution of linear indeterminate equations, of Brahmagupta (c.628) on the diagonals and the area of a cyclic quadrilateral and of Bhàskara (c.1150) on the surface area and volume of a sphere.

The Astronomy part is divided into eight Chapters and the topics covered are Grahagati (computation of mean and true longitudes of planets), Bhågola and Bhagola (Earth and celestial spheres), problems relating to right ascension, declination, longitude, etc, determination of time, place, direction, etc., from gnomonic shadow), eclipses, phases of the Moon, and so on. A distinguishing feature of this work is that it gives a detailed exposition of the revised planetary model proposed by Nãlakaõñha which, for the first time in the History of Astronomy, gives the correct formulation of the equation of centre and the latitudinal motion of the interior planets, Mercury and Venus."

A wonderful addition to our History of Science and Mathematics sections. ISBN 978-81-85931-83-8