Lilavati
Lilavati (also Leelavati, Sanskrit: लीलावती, Līlāvatī) was Indian mathematician Bhāskara II's treatise on mathematics. It is the first volume of his main work Siddhānta Shiromani, Sanskrit for "Crown of treatises,"[1] alongside Bijaganita, Grahaganita and Golādhyāya.[2]
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[edit] Name
His book on arithmetic is the source of interesting legends that assert that it was written for his daughter, Lilavati. In one of these stories, which is found in a Persian translation of Lilavati, Bhaskara II studied Lilavati's horoscope and predicted that her husband would die soon after the marriage if the marriage did not take place at a particular time. To alert his daughter at the correct time, he placed a cup with a small hole at the bottom of a vessel filled with water, arranged so that the cup would sink at the beginning of the propitious hour. He put the device in a room with a warning to Lilavati to not go near it. In her curiosity though, she went to look at the device and a pearl from her nose ring accidentally dropped into it, thus upsetting it. The marriage took place at the wrong time and she was soon widowed.
Many of the problems are addressed to Līlāvatī herself who must have been a very bright young woman. For example "Oh Līlāvatī, intelligent girl, if you understand addition and subtraction, tell me the sum of the amounts 2, 5, 32, 193, 18, 10, and 100, as well as [the remainder of] those when subtracted from 10000." and "Fawn-eyed child Līlāvatī, tell me, how much is the number [resulting from] 135 multiplied by 12, if you understand multiplication by separate parts and by separate digits. And tell [me], beautiful one, how much is that product divided by the same multiplier?"
The word Līlāvatī itself means beautiful or one possessing beauty (from Sanskrit, Līlā = beautiful, -vatī = female possessing the quality).
[edit] Contents
The book contains thirteen chapters, mainly definitions, arithmetical terms, interest computation, arithmetical and geometrical progressions, plane geometry, solid geometry, the shadow of the gnomon, the kuttaka - a method to solve indeterminate equations, and combinations.
Lilavati includes a number of methods of computing numbers such as multiplications, squares, and progressions, with examples using kings and elephants, objects which a common man could understand.
Excerpt from Lilavati (Appears as an additional problem attached to stanza 54, Chapter 3. Translated by T N Colebrook)
Whilst making love a necklace broke.
A row of pearls mislaid.
One sixth fell to the floor.
One fifth upon the bed.
The young woman saved one third of them.
One tenth were caught by her lover.
If six pearls remained upon the string
How many pearls were there altogether?
Bhaskaracharya's conclusion to Lilavati states:
Joy and happiness is indeed ever increasing in this world for those who have Lilavati clasped to their throats, decorated as the members are with neat reduction of fractions, multiplication and involution, pure and perfect as are the solutions, and tasteful as is the speech which is exemplified.
[edit] Translations
The translations or editions of the Lilavati into English include:
- 1816. John Taylor, Lilawati: or A Treatise on Arithmetic or Geometry by Bhascara Acharya
- 1817. Henry Thomas Colebrooke, Algebra, with Arithmetic and mensuration, from the Sanscrit of Brahmegupta and Bháscara
- 1975. K. V. Sarma, Līlāvatī of Bhāskarācārya with Kriyā-kramakarī, Hoshiarpur: VVBIS & IS, Panjab University
- 2001. K. S. Patwardhan, S. A. Naimpally and S. L. Singh. Līlāvatī of Bhāskarācārya: a treatise of mathematics of Vedic tradition : with rationale in terms of modern mathematics largely based on N.H. Phadke's Marāthī translation of Līlāvatī
[edit] See also
[edit] References
- ^ Plofker 2009, p. 71.
- ^ Poulose 1991, p. 79.
[edit] External links
- Lilavati of Bhaskaracharya-Original Book in English Translation
- Bhaskaracharya's Lilavathi - Book Review
- Bhaskara
- Khagol Mandal
