Lilavati of Bhaskaracarya A Treatise of Mathematics of Vedic Tradition : With Rationale in Terms of Modern Mathematics

Contents: Foreword. Preface. Bhaskaracarya: his life and work. Lilavati. 1.Definitions of tables. 2. Place values of digits. 3. Addition and subtraction. 4. Methods of multiplication. 5. Division. 6. Methods of finding squares. 7. Square root. 8. Method to find the cube. 9. Cube roots.10. Eight operations on fractions. 11. Addition and subtraction of fractions. 12. Multiplication fractions. 13. Division of fractions. 14. Squares, cubes, square roots and cube roots of fractions. 15. Eight rules concerning zero. 16. Reverse process. 17. To find an unknown quantity. 18. Method of transition. 19. Square transition. 20. Quadratic equation. 21. The rule of three. 22. Inverse proportion. 23. The rule of five. 24. Rules for barter. 25. Simple interest. 26. Combinations. 27. Progressions ( series). 28. Mensuration. 29. Volume. 30. Wood cutting. 31. Volume of a heap of grain. 32. Shadows. 33. Pulverization. 34. Concatenation ( permutations, partitions etc.). Index of verses. Subject index.Motilal Banarsidass. Lilavati has been used as a standard textbook for about 800 years. Itwas widely used and commented and translated into several languages of the world. Arithmetic is presented as an enjoyable playful activity. The name 'Bhaskaracarya' and 'Lilavati' are well-known. Aryabhata (b.476 AD) is credited for his pioneering work of extracting tantra sastra, (I.e. astronomy and mathematics) from vedas (generally known as the oldest embodiment of knowledge) to the level of common usage as he appropriately says in his Aryabhatiyam.In 1150 AD, Bhaskaracarya (b.1114 AD), renowned mathematician and astronomer of Vedic tradition composed Lilavati as the first part of this larger world called Siddhanta-Siromani, a comprehensive exposition of arithmetic, algebra, geometry, mensuration, number theory and related topics, 201 pp. The names 'Bhaskaracarya' and 'Lilavati' are well-known. If a student displays outstanding talent in Mathematics, the school teacher lovingly calls the student ÏSecond BhaskaracaryaÓ. Many legends about Lilavati are in vogue. It is but natural that Indians have a special interest in Bhaskaracarya and his works, especially the Lilavati. Professor N.H. Phadke has taken great pains in the preparation of the present work A New Light on Lilavati, thus filling a void. In the Lilavati, Arithmetic is presented as an enjoyable playful activity. Professor Phadke has admirably succeeded in preserving this spirit in the A New Light on Lilavati. Since Professor Phadke studied many books in Sanskrit, Hindi, English and Marathi, he could have easily given scholarly notes and references all over. But the author has resisted that temptation and has given the relevant supplementary information in six appendices. So the book is easy to read and the readers enjoy the playful atmosphere. The Lilavati is a book on Arithmetic written in the twelfth century. Techniques for the solution of problems are simple and easy to use and, moreover, there is a lot of interesting information in the problems presented therein. In 1150 AD, Bhaskaracarya (b. 1114 AD), renowned mathematician and astronomer of Vedic tradition composed Lilavati as the first part of his larger work called Siddhanta Siromani, a comprehensive exposition of arithmetic, algebra, geometry, mensuration, number theory and related topics. Lilavati has been used as a standard textbook for about 800 years. This lucid, scholarly and literary presentation has been translated into several languages of the world. Bhaskaracarya himself never gave any derivations of his formulae. N.H. Phadke (1902-1973) worked hard to construct proofs of several mathematical methods and formulae given in original Lilavati. The present work is an enlargement of his Marathi work and attempts a thorough mathematical explanation of definitions, formulae, short cuts and methodology as intended by Bhaskara. Stitches are followed by literal translations so that the reader can enjoy and appreciate the beauty of accurate and musical presentation in Lilavati. The book is useful to school going children, sophomores, teachers, scholars, historians and those working for cause of mathematics.