Līlāvatī of Bhāskara

Introduction

Līlāvatī is Indian mathematician Bhāskara II's treatise on gaṇita-śāstra (mathematics) written in 1150. The word Līlāvatī is a feminine form of the word Līlāvat which is a taddhita formation from the word Līlā. The word Līlā denotes many meanings such as 'play, sport, amusement' and also 'charm, grace, beauty etc. The latter meanings viz. 'charm, grace, beauty' etc. are more suitable in the present context since it is feminine; and the derivative Lilavatī will mean one 'possessed of charm, grace or beauty' etc. Līlāvatī is the first part of Bhaskarācārya's work on Siddhāntaśiromaṇi. Siddhāntaśiromaṇi consists of four parts which are 1. Līlāvatī, 2. Bījagaṇita, 3.Gaṇitādhyāya and 4. Golādhyāya. This is depicted in the below table.

Gaṇita
Applied Mathematics (Applied to Astronomy)		Pure Mathematics
Gaṇitādhyāya		Vyaktagaṇita (Līlāvatī)		Avyaktagaṇita (Bījagaṇita)
Golādhyāya

Vyaktagaṇita is also called as Pāṭīgaṇita or Aṅkagaṇita.

Līlāvatī has an interesting story associated with how it got its name. Bhaskarācārya created a horoscope for his daughter Līlāvatī , stating exactly when she needed to get married. He placed a cup with a small hole in it in a tub of water, and the time at which the cup sank was the optimum time Līlāvatī was to get married. Unfortunately, a pearl fell into the cup, blocking the hole and keeping it from sinking. Līlāvatī was then doomed never to wed, and her father Bhāskara wrote her a manual on mathematics in order to console her, and named it Līlāvatī . This appears to be a myth associated with this classical work.

Literary qualities of the text

The text of Līlāvatī is composed in verse and not in prose, as has been the practice of the ancient Indian Sanskrit scientists. The only motive behind the text to be in verse is , the knowledge was handed down orally, poetry proved to be of great value and convenience in oral traditions. In spite of the dry and purely theoretical nature of the science of mathematics, Bhaskarācārya seems to have tried to bring as much literary charm in his compositions as possible, and his versification does exhibit certain literary qualities and merits.

Contents of Līlāvatī

Lilavati mainly deals with ‘Arithmetic’ in today’s mathematical parlance. It consists of 279 verses written in Sanskrit in poetic form. There are certain verses which deal with Mensuration (measurement of various geometrical objects), Volume of pyramid, cylinders, heaps of grains etc., wood cutting, shadows, trigonometric relations and also on certain elements of Algebra such as finding an unknown quantity subject to certain constraints using the method of supposition.

See Also

भास्कर की 'लीलावती'