Twelfth-century mathematics, rebuilt in modern notation. Bhaskara II wrote Lilavati as a book of story problems about bees, peacocks and broken bamboo, and this 29-page companion maps its topics and works through 11 of those problems step by step.
What brings you to Lilavati?
Each worked problem states the setup in Bhaskara's words and follows it with a modern symbolic solution, so you can check every step.
Section 4
Definitions and operations, fractions, zero and negative numbers, roots, progressions, plane and solid geometry, the shadow of the gnomon, combinations and the net of numbers.
Section 5
The Beautiful Maiden's Riddle, the Peacock and the Snake, the Bees and the Lotus, the Broken Bamboo, the Lotus in the Pool, the Monkey and the Tree, and the Division of Gems.
Section 6
The Rule of Three, the Kuttaka (pulverizer) for indeterminate equations, Bhaskara's treatment of surds and the Chakravala method as companion material.
Section 7
How Lilavati treats zero, negative numbers and iterative algorithms, with a cautious note on rate-of-change ideas in Bhaskara's astronomy.
Sections 8 to 11
How the work travelled to the Islamic world and Europe, how it compares with Greek and Chinese mathematics, and why the problems still teach well.
Appendices
A timeline of Indian mathematics from the Sulba Sutras to the Kerala school, Bhaskara's approximation for sine and four practice problems.
This is a reconstruction in modern notation, not a scholarly translation of the Sanskrit. Methods and astronomical notes from beyond Lilavati's arithmetic are clearly labeled as companion material.
Every problem comes with a worked solution, and the methods come with diagrams. You can open any page at full size.
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The book moves from the story to the solving to the methods, so the history makes sense once you have done the mathematics.
Sections 1 to 4
Who Bhaskara II was, the legend behind the name Lilavati and how the work is organized into 13 topics.
You leave with: a map of what Lilavati covers before you start solving.
Section 5
Seven famous story problems, each with the original setup and a modern solution you can follow line by line.
You leave with: the problems solved, and the habit of checking an answer against the story.
Sections 6 and 7
The Rule of Three, the Kuttaka, surds and the Chakravala, then the ideas that ran ahead of their time.
You leave with: methods you can reuse on new problems.
Sections 8 to 12 and the appendices
Four more problems, the book’s influence, comparisons with Greece and China, and a timeline.
You leave with: the context, ten references to check and four problems to try alone.
Each group opens to its sections, and the filter finds a topic or a problem across all of them.
Who wrote Lilavati, the legend behind it and how it is organized.
Seven story problems with their original setups and modern solutions.
The tools behind the problems, and the ideas that ran ahead of their time.
Where the work travelled and how it compares.
Ten references and three appendices.
Nothing matches that yet. Try a broader word such as problem, method or geometry.
It is written for people who want to work the problems. If you need a critical edition, it isn't that book.
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Problems and Solutions in Modern Notation
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Yes. There is no payment anywhere. The free checkout creates your order and keeps the PDF in your account.
The checkout puts the file in your account, so the link keeps working and you can download it again later. It needs a name and an email address and no payment details.
No. The PDF uses English and modern notation. It is an educational companion, not a Sanskrit edition or a line-by-line scholarly translation.
Mathematics first. The context is there, with comparisons to Greek and Chinese traditions and a timeline from the Sulba Sutras onward, but the core of the book is working through the problems and the methods.
Chakravala is a cyclic method from the wider Indian tradition for solving indeterminate equations such as Pell's equation. The PDF treats it as companion material, alongside Kuttaka, without claiming every method discussed belongs to Lilavati itself.
School algebra and the Pythagorean theorem cover nearly everything. A few method notes use more symbols, and you can skip those on a first read.
The Broken Bamboo has been waiting since the 12th century. The PDF is free, and the download takes a minute.
Bhaskaracharya's Lilavati
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