Finding Unknowns in Medieval India: A Dialogue
摘要
We present a dialogue in two scenes between the twelfth-century Indian mathematician Bhāskara II and his daughter Lı̄lāvatı̄, based on his writings. Bhāskara teaches his daughter from his Lı̄lāvatı̄ and his Bı̄jagaṇita, starting with arithmetical calculation and leading on naturally to algebra. The lesson culminates in the solution of simultaneous linear equations and even a quadratic. Negatives and calculations with zero are featured, and perhaps the first recorded tentative recognition of a negative root of a quadratic equation. The aim is not only to demonstrate the technical innovations of Bhāskara and his contemporaries, but also to display Indian cultural perceptions of mathematics and some fundamental aspects of mathematical style and practice. Bhāskara’s books are written in the terse Indian verse tradition, and the origins of this are described in a survey of the long history of Indian mathematics. We aim to preserve as much as possible of his style in the dialogue, while giving transcriptions of the procedures in modern mathematical notation. Bhāskara’s work is a foretaste of the great achievement reflected in our modern procedures in which negative roots and multiple solutions are fully accepted. The dialogue can be used in a modern classroom, and is designed to bring the mathematics to life in its context. Such a mathematical play can demonstrate the power of theatre (and history of mathematics) to motivate learners in algebra.