Veda, by definition, is ‘knowledge’. Hence
Vedic Math has a much ancient origin though attributed
to the techniques rediscovered between 1911-1918 (see
January 2003 column in Lotus). Mathematicians from
across the spectrum from Hindu, Buddha and Jaina subcultures
have contributed immensely to this body of
knowledge. To learn about Vedic Math in these columns,
I have two objectives.
I. First is to give a sense of the extent of
accomplishments of these scholars and rishis to
the readers. This I will do so by discussing
known works.
II. The second, and a continuing quest in these
columns is to illustrate one technique of Vedic
Math each time.
BHASKARA’S LILAVATI - A MATHEMATICAL
TREATISE
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 distill
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 of
multiplication
What is the product of 135 and 12?
Also, tell me what number will you obtain when the
product 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 the
half 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 were
sporting 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.


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