Bhaskara’s LILAVATI

Of the many scholars Bhaskaracharya or Bhaskara II (1114-1193 C.E.) stands out as a teacher and poet. According to the description in his book ‘Philosophical Crown Jewel’ [Sidhantashiromani] he lived either in Southern India – probably south of modern day Bombay. Under the able tutelage of his father and teacher Maheshwara a great astronomer, young Bhaskara mastered mathematics, astronomy, Panini (Sanskrit) grammar, and poetry. This treatise

written when Bhaskara was 36, consists of four parts:

Arithmetic (Lilavati), Algebra (Bijaganita), Celestial Globe (Goladhyaya), and Planetary Mathematics (Grahaganita).

Among these Lilavati stands out. The beauty of Lilavati is that Bhaskara has been able to distil mathematics into a poetry form with 261 slokas or verses. This great mathematician was an excellent teacher as well, as the two examples below illustrate:

1. In the XVIII’th stanza of Lilavati the author says:

O! you auspicious girl with enchanting eyes of a fawn, Lilavati,

If you have well understood the above methods ofmultiplication

What is the product of 135 and 12?

Also, tell me what number will you obtain when theproduct is divided by 12.

2. In the LIV’th stanza of Lilavati the author gives a ‘word problem’:

Of a group of elephants, half and one third of thehalf went into a cave,

One sixth and one seventh of one sixth was drinking water from a river.

One eight and one ninth of one eighth weresporting in a pond full of lotuses

The lover king of the elephants was leading three female elephants; [then], how many elephants were there in the flock?

Now the reader may be wondering who in the world was ‘Lilavati’? According to a 1587 translation by Fyzi (an Arab translator) Lilavati was Bhaskara’s daughter. A famed astronomer and astrologer, Bhaskara foresaw that his daughter would not be married and live happily if she is not wedded at an auspicious moment. To find the moment, he constructed a device – a cup with a small hole in its bottom that was placed in a vessel filled with water. The auspicious moment would be when the cup that would sink having slowly filled-up. As fate would have it, on the wedding day, a pearl from Lilavati’s dress fell into the cup and blocked the hole and the auspicious moment passed without her getting married. Bhaskara then wrote Lilavati to console and detract his grief stricken daughter to whom he taught the mathematical techniques.As the book demonstrates, Bhaskara though a masterful mathematician, was also a rasika as his poetry indicates. He teaches his pupil to be mindful of her surroundings by formulating relevant contextual word problems in arithmetic, algebra and geometry – a clear expert in pedagogy. His book has been used as a

standard mathematical text in Indian Gurukulas (traditional schools) for the last eight hundred years.

– Taken from N.Sreenaths Article on Vedic mathematics


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