HOME

TheInfoList



OR:

''Līlāvatī'' is a treatise by Indian mathematician
Bhāskara II Bhāskara II ('; 1114–1185), also known as Bhāskarāchārya (), was an Indian people, Indian polymath, Indian mathematicians, mathematician, astronomer and engineer. From verses in his main work, Siddhānta Śiromaṇi, it can be inferre ...
on mathematics, written in 1150 AD. It is the first volume of his main work, the '' Siddhānta Shiromani'', alongside the '' Bijaganita'', the ''Grahaganita'' and the ''Golādhyāya''.


Name

Bhaskara II's book on
arithmetic Arithmetic is an elementary branch of mathematics that deals with numerical operations like addition, subtraction, multiplication, and division. In a wider sense, it also includes exponentiation, extraction of roots, and taking logarithms. ...
is the subject of interesting legends that assert that it was written for his daughter, Lilavati. As the story goes, the author had studied Lilavati's
horoscope A horoscope (or other commonly used names for the horoscope in English include natal chart, astrological chart, astro-chart, celestial map, sky-map, star-chart, cosmogram, vitasphere, radical chart, radix, chart wheel or simply chart) is an ast ...
and predicted that she would remain both childless and unmarried. To avoid this fate, he ascertained an auspicious moment for his daughter's wedding. 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. A pearl from her bridal dress accidentally dropped into it, thus upsetting it. The auspicious moment for the wedding thus passed unnoticed leaving Bhaskara II devastated. Thus, he promised his daughter to write a book in her name, one that would remain till the end of time as a good name is akin to a second life. 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 he remainder ofthose when subtracted from 10000." and "Fawn-eyed child Līlāvatī, tell me, how much is the number esulting from135 multiplied by 12, if you understand
multiplication Multiplication is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division (mathematics), division. The result of a multiplication operation is called a ''Product (mathem ...
by separate parts and by separate digits. And tell e beautiful one, how much is that product divided by the same multiplier?" The word ''Līlāvatī'' itself means playful or one possessing play (from Sanskrit, Līlā = play, -vatī = female possessing the quality).


Contents

The book contains thirteen chapters, mainly definitions, arithmetical terms, interest computation, arithmetical and geometrical progressions,
plane geometry Euclidean geometry is a mathematical system attributed to ancient Greek mathematics, Greek mathematician Euclid, which he described in his textbook on geometry, ''Euclid's Elements, Elements''. Euclid's approach consists in assuming a small set ...
,
solid geometry Solid geometry or stereometry is the geometry of Three-dimensional space, three-dimensional Euclidean space (3D space). A solid figure is the region (mathematics), region of 3D space bounded by a two-dimensional closed surface; for example, a ...
, the shadow of the
gnomon A gnomon (; ) is the part of a sundial that casts a shadow. The term is used for a variety of purposes in mathematics and other fields, typically to measure directions, position, or time. History A painted stick dating from 2300 BC that was ...
, the
Kuṭṭaka Kuṭṭaka is an algorithm for finding integer solutions of linear Diophantine equations. A linear Diophantine equation is an equation of the form ''ax'' + ''by'' = ''c'' where ''x'' and ''y'' are unknown quantities and ''a'', ''b'', and ''c'' ar ...
- a method to solve indeterminate equations, and combinations. Bhaskara II gives the value of pi as 22/7 in the book but suggest a more accurate ratio of 3927/1250 for use in astronomical calculations. Also according to the book, the largest number is the ''parardha'' equal to one hundred thousand billion. ''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
fraction A fraction (from , "broken") represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, a fraction describes how many parts of a certain size there are, for example, one-half, eight-fifths, thre ...
s,
multiplication Multiplication is one of the four elementary mathematical operations of arithmetic, with the other ones being addition, subtraction, and division (mathematics), division. The result of a multiplication operation is called a ''Product (mathem ...
and
involution Involution may refer to: Mathematics * Involution (mathematics), a function that is its own inverse * Involution algebra, a *-algebra: a type of algebraic structure * Involute, a construction in the differential geometry of curves * Exponentiati ...
, pure and perfect as are the solutions, and tasteful as is the speech which is exemplified.


Translations

The translations or editions of the Lilavati into English and other languages include: * 1816. John Taylor
''Lilawati: or A Treatise on Arithmetic or Geometry by Bhascara Acharya''
* 11th century: Eluganti Pedana ( ఎలుగంటి పెద్దన) translated Lilavati into Telugu. The work is called Prakīrna Ganitamu( ప్రకిర్ణ గణితము). * 1817.
Henry Thomas Colebrooke Henry Thomas Colebrooke FRS FRSE FLS (15 June 1765 – 10 March 1837) was an English orientalist and botanist. He has been described as "the first great Sanskrit scholar in Europe". Biography Henry Thomas Colebrooke was born on 15 June ...

''Algebra, with Arithmetic and mensuration, from the Sanscrit of Brahmegupta and Bháscara, Page 24, chap 2/3''
* 1842. Amichandra Shravaga of Jaipur translated ''Lilavati'' into Hindi. * 1936. Pidaparti Krishnamurti Sastry translated the work into Telugu language and it was published by Srividya press, Vizianagaram. * 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
*Bhaskaracharya's work 'Lilavati' was translated into Persian(फारसी) by-( Abul Faizi-in 1587 ). *Bakul Kayastha from medieval Assam (1400CE) made Assamese rendering of Lilavati.


See also

*
Indian mathematics Indian mathematics emerged in the Indian subcontinent from 1200 BCE until the end of the 18th century. In the classical period of Indian mathematics (400 CE to 1200 CE), important contributions were made by scholars like Aryabhata, Brahmagupta, ...
* Timeline of algebra and geometry


References


Works cited

* *


External links


Bhaskaracharya's Lilavathi
- Book Review
Khagol Mandal
{{DEFAULTSORT:Lilavati Indian mathematics Social history of India Science and technology in India 12th-century books 12th-century Sanskrit literature