Lilavati
Encyclopedia
Lilavati 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," alongside Bijaganita
, Grahaganita and Golādhyāya.
The word Līlāvatī itself means beautiful or one possessing beauty (from Sanskrit, Līlā = beautiful, -vatī = female possessing the quality).
, 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:
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
. It is the first volume of his main work Siddhānta Shiromani
Siddhānta Shiromani
Siddhānta Shiromani is the major work of Indian mathematician Bhāskara II.Bhaskaracharya wrote Siddhanta Shiromani in 1150 AD when he was 36 years old. This is a mammoth work containing about 1450 verses.-Lilavati:...
, Sanskrit
Sanskrit
Sanskrit , is a historical Indo-Aryan language and the primary liturgical language of Hinduism, Jainism and Buddhism.Buddhism: besides Pali, see Buddhist Hybrid Sanskrit Today, it is listed as one of the 22 scheduled languages of India and is an official language of the state of Uttarakhand...
for "Crown of treatises," alongside Bijaganita
Bijaganita
Bijaganita was Indian mathematician Bhāskara II's treatise on algebra. It is the second volume of his main work Siddhānta Shiromani, Sanskrit for "Crown of treatises," alongside Lilāvati, Grahaganita and Golādhyāya.- Contents :...
, Grahaganita and Golādhyāya.
Name
The name comes from his daughter Līlāvatī. 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).
Contents
The book contains thirteen chapters, mainly definitions, arithmetical terms, interest computation, arithmetical and geometrical progressions, plane geometryPlane geometry
In mathematics, plane geometry may refer to:*Euclidean plane geometry, the geometry of plane figures,*geometry of a plane,or sometimes:*geometry of a projective plane, most commonly the real projective plane but possibly the complex projective plane, Fano plane or others;*geometry of the hyperbolic...
, solid geometry
Solid geometry
In mathematics, solid geometry was the traditional name for the geometry of three-dimensional Euclidean space — for practical purposes the kind of space we live in. It was developed following the development of plane 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 fractionFraction (mathematics)A fraction represents a part of a whole or, more generally, any number of equal parts. When spoken in everyday English, we specify how many parts of a certain size there are, for example, one-half, five-eighths and three-quarters.A common or "vulgar" fraction, such as 1/2, 5/8, 3/4, etc., consists...
s, multiplicationMultiplicationMultiplication is the mathematical operation of scaling one number by another. It is one of the four basic operations in elementary arithmetic ....
and involution, 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 include:- 1816. John Taylor, Lilawati: or A Treatise on Arithmetic or Geometry by Bhascara Acharya
- 1817. Henry Thomas ColebrookeHenry Thomas ColebrookeHenry Thomas Colebrooke was an English orientalist.-Biography:Henry Thomas Colebrooke, third son of Sir George Colebrooke, 2nd Baronet, was born in London. He was educated at home; and when only fifteen he had made considerable attainments in classics and mathematics...
, Algebra, with Arithmetic and mensuration, from the Sanscrit of Brahmegupta and Bháscara - 1975. K. V. SarmaK. V. SarmaK. V. Sarma was an Indian historian of science, particularly the astronomy and mathematics of the Kerala school.His doctoral thesis was at the Panjab University in 1977....
, Līlāvatī of Bhāskarācārya with Kriyā-kramakarīKriyakramakariKriyakramakari is an elaborate commentary in Sanskrit written by Sankara Variar and Narayana, two astronomer-mathematicians belonging to the Kerala school of astronomy and mathematics, on Bhaskara II's well-known textbook on mathematics Lilavati...
, 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
External links
- Lilavati of Bhaskaracharya-Original Book in English Translation
- Bhaskaracharya's Lilavathi - Book Review
- Bhaskara
- Khagol Mandal