Bhaskaracharya
popularly known as Bhaskara, was a famous mathematician &
astronomer of ancient India. He was born in the Bijapur district of
Karnataka. Bhaskara represented the peak of mathematical knowledge in
the 12th century & was the head of the astronomical observatory at
Ujjain, the leading mathematical centre of ancient India. It is believed
that Bhaskara learned Mathematics from his father Mahesvara, an
astrologer. Bhaskara imparted his knowledge of mathematics to his son
Lokasamudra who had started a school to study the works of his father.

Bhaskara
wrote the books "SIDDHANTA SIROMANI", "LILAVATI" & "BIJAGANITA".
The first book mainly deals with astronomy & other were on
Mathematics. "SIDDHANTA SIROMANI" was written in the year 1150 &
consists of two parts GOLADHYAYA (sphere) & GRAHAGANITA (Mathematics
of the planets). This book also deals with many other concepts like
Trigonometry & Calculus.

Lilavati
(meaning a beautiful woman) is based on Arithmetic. It is believed that
Bhaskara named this book after his daughter Lilavati. Many of the
problems in this book are addressed to his daughter. For example "Oh
Lilavati, intelligent girl, if you understand addition &
subtraction, tell me the sum of the amounts 2, 5, 32, 193, 18, 10 &
100, as well as [the remainder of] those when subtracted from 10000."
The book contains thirteen chapters, mainly definitions, arithmetical
terms, interest computation, arithmetical & geometric progressions.
Many of the methods in the book on computing numbers such as
multiplications, squares & progressions were based on common objects
like kings & elephants, which a common man could understand.

Bijaganita
is on Algebra & contains 12 chapters. "A positive number has two
square-roots (a negative root & a positive root)". This was
published in this text for the very first time. It contains concepts of
positive & negative numbers, zero, the 'unknown' (includes
determining unknown quantities), surds, simple equations & quadratic
equations.

Bhaskara
was the first to introduce the concept of infinity - if any finite
number is divided by zero, the result is infinity. Also the fact that if
any finite number is added to infinity then the sum is infinity. He
developed a proof of the Pythogorean theorem by calculating the same
area in two different ways & then cancelling out two terms to get
a^2 + b^2 = c^2. He is also known for his calculation of the time
required (365.2588 days) by the Earth to orbit the Sun which differs
from the modern day calculation of 365.2563 days, by just 3.5 minutes!
The law of Gravitation had been proved by Bhaskara 500 years before it
was rediscovered by Newton.

Bhaskara,
a significant contributor to the world of astronomy & mathematics,
was also a poet like many Indian mathematicians of his time. He had the
habit of posing his questions in the form of interesting riddles. Here
is one such question.

Try solving it...

Out
of a group of swans, 7/2 times the square root of the number are
playing on the shore of a tank. The two remaining ones are playing with
amorous fight, in the water.

What is the total number of swans?

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