Saturday, 16 February 2013

Bhaskaracharya - Greatest mathematician

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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