Foreword

Summary

Although the Middle Ages are often thought of as a period of little progress in mathematics, the statement is true only of Europe; much progress was made in other parts of the world. The first three papers in this section deal with the contributions of medieval south Indian mathematicians to the development of the power series representation of the sine, cosine, and arctangent series; these power series first occur in a work by Nilakantha in the early sixteenth century. A detailed derivation of the series appeared later in that century in a work of Jyesthadeva, who attributed the series to the fourteenth-century mathematician Madhava. This Indian work was first brought to the attention of western scholars by C. M. Whish in 1835, but his work had no effect. They were reintroduced to Europe in a series of articles by C. Rajagopal and his associates beginning in 1949.

The article by Ranjan Roy discusses the derivation of the arctangent formula and its application to finding a series approximation to π. Roy also discusses the analogous work by Gottfried Leibniz around 1675 and by James Gregory a few years earlier. Victor Katz's article concentrates on the derivation of the sine and cosine series. Since it was necessary for the derivation of all three series for the Indian mathematicians to have some knowledge of formulas for the sum of integral powers, Katz discusses one particular derivation of such formulas. This was the work of Ibn al-Haytham, known to the West as Alhazen, a mathematician who worked in Egypt around the year 1000.