✦ LIBER ✦
An Example of the Secant Method of Iterative Approximation in a Fifteenth-Century Sanskrit Text
✍ Scribed by Kim Plofker
- Publisher
- Elsevier Science
- Year
- 1996
- Tongue
- English
- Weight
- 178 KB
- Volume
- 23
- Category
- Article
- ISSN
- 0315-0860
No coin nor oath required. For personal study only.
✦ Synopsis
Mathematical approximation by iterative algorithms is well attested in Sanskrit astronomical texts, but its use has not been studied systematically. In his 14th-century supercommentary on Govindasva ¯min's commentary on Bha ¯skara I's Maha ¯bha ¯skarı ¯ya, Parames ´vara, a student of the renowned Kerala astronomer Ma ¯dhava, presents a one-point iterative technique for calculating the Sine of a given angle, as well as a modification of this technique that involves a two-point algorithm essentially identical to the modern secant method. This paper presents a mathematical and historical interpretation of his remarks.