mathematics

Līlāvatī

Līlāvatī is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Līlāvatī rather than just read about it. In short: Līlāvatī is a treatise by Indian mathematician Bhāskara II 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.

Key takeaways

Līlāvatī belongs to mathematics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Līlāvatī to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Līlāvatī from memory before moving on to harder problems.

Reference excerpt

Līlāvatī is a treatise by Indian mathematician Bhāskara II 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.

The Leelavati Award is named after this treatise.

Name Bhaskara II's book on arithmetic 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 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 [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 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, solid geometry, the shadow of the gnomon, the Kuṭṭaka - 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)

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.

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, 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 Timeline of algebra and geometry

References

Works cited Plofker, Kim (2009), Mathematics in India, Princeton University Press, ISBN 9780691120676 Poulose, K. G., ed. (1991), Scientific heritage of India, mathematics, Ravivarma Samskr̥ta granthāvali, vol. 22, Govt. Sanskrit College (Tripunithura, India)

External links Bhaskaracharya's Lilavathi - Book Review Bhaskara Khagol Mandal

Illustrations

Worked examples

Example 1 — a first encounter with Līlāvatī

Start with the simplest possible case. Write down what Līlāvatī claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Līlāvatī before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Līlāvatī ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Līlāvatī

In research: Līlāvatī appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Līlāvatī in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Līlāvatī is common in secondary-school and first-year university syllabi. It links to neighbouring topics 12th-century Sanskrit literature, 12th-century books, Indian mathematics, so understanding it makes those chapters shorter.
In everyday life: Look for Līlāvatī outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Līlāvatī in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Līlāvatī means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Līlāvatī out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Līlāvatī in simple terms?

Why does Līlāvatī matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Līlāvatī?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Līlāvatī.