• Takao Hayashi
Living reference work entry
DOI: https://doi.org/10.1007/978-94-007-3934-5_9263-2

The Līlāvatī is a Sanskrit work on arithmetic and mensuration (computational geometry) composed in or a little before AD 1150 by Bhāskara II, one of the greatest Indian mathematician-astronomers. The Līlāvatī is sometimes regarded as the first part of the Siddhāntaśiromaṇi, a masterpiece on gaṇita (mathematics) in its broad sense (including mathematical astronomy), the other parts being Bījagaṇita, Grahagaṇitādhyāya (chapter on planetary computation), and Golādhyāya (chapter on spherical astronomy), but in manuscripts the four parts have been handed down to us independently.

In medieval India, mathematics proper comprised two major fields, pāṭīgaṇita (mathematics of algorithm) and bījagaṇita (“mathematics of seeds” or algebra). The Līlāvatī is the most typical and the most influential work of pāṭīgaṇita. More than 600 manuscripts of the work reported so far and more than 30 extant commentaries attest that it was the most popular mathematical textbook in India used by a number of...


Orange Peel Mathematical Textbook Pythagorean Theorem Natural Series Similar Triangle 
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  1. Colebrooke, H. T. (2005). Algebra with arithmetic and mensuration from the Sanscrit of Brahmegupta and Bhāscara. London: Murray, 1817. Rpt, Wiesbaden: Martin Sändig 1973. Rpt (with the title, Classics of Indian mathematics: Algebra, with arithmetic and mensuration, from the sanskrit of Brahmagupta and Bhāskara, and with a Foreword by S. R. Sarma). Delhi, India: Sharada Publishing House.Google Scholar
  2. Hayashi, T. (1995). The Bakhshālī manuscript: An ancient Indian mathematical treatise (Groningen oriental studies, Vol. 11). Groningen, the Netherlands: Egbert Forsten.Google Scholar
  3. Hayashi, T. (1997). Calculations of the surface of a sphere in India. The Science and Engineering Review of Doshisha University, 37(4), 194–238.Google Scholar
  4. Hayashi, T. (2002). Notes on the differences between the two recensions of the Līlāvatī of Bhāskara II. SCIAMVS, 3, 193–230.Google Scholar
  5. Hayashi, T. (2009). Bījagaṇita of Bhāskara. SCIAMVS, 10, 3–301.Google Scholar
  6. Bhāskara (Bhāskara II, Bhāskarācārya). (1975). Līlāvatī. Edited with the commentaries of Gaṇeśa and of Mahīdhara by D. Āpaṭe. Ānandāśrama Sanskrit series, Vol. 107. Poona, India: Ānandāśrama 1937. Also edited with the commentary of Śaṅkara and Nārāyaṇa by K. V. Sarma. Vishveshvaranand Indological series, Vol. 66. Hoshiarpur, India: Vishveshvaranand Vedic Research Institute.Google Scholar
  7. Patwardhan, K. S., Naimpally, S. A., & Singh, S. L. (2001). Līlāvatī of Bhāskarācārya: A treatise of mathematics of Vedic tradition with rationale in terms of modern mathematics largely based on N. H. Phadke’s Marāṭhī translation of Līlāvatī (pp. 168–174). Delhi, India: Motilal (Reviewed by T. Hayashi, Historia Scientiarum 12.2).Google Scholar
  8. Pingree, D. (1970–1994). Census of the exact sciences in Sanskrit, series A (Vols. 1–5). Philadelphia, PA: American Philosophical Society.Google Scholar
  9. Sarma, S. R. (2006). Mathematics and iconography in Līlāvatī 263. Journal of the Asiatic Society of Mumbai, 80, 115–126.Google Scholar
  10. Xu Zelin et al. (2008). Līlāvatī (Chinese translation). Beijing, China: Science Press. (徐澤林等訳《莉拉沃蒂》北京: 科學出版社, 2008)Google Scholar

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© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Doshisha UniversityKyoto CityJapan