Sunday, November 4, 2018

Bhaskaracharya discoveres Infinity


Bhaskaracharya discoveres Infinity .....
Bhaskara was the first to introduce the concept of Infinity: If any finite number is divided by zero, the result is infinity
Bhaskaracharya, the greatest Mathematician who introduced concept of ‘Infinity’Bhaskaracharya (Bhāskara the teacher) was an Bharatiya mathematician and astronomer of 12th century AD.
He is refered as Bhāskara II to avoid confusion with Bhāskara I (of 7th century AD). He was born near Vijjadavida (Bijapur in modern Karnataka) and lived between 1114-1185 AD. Bhaskaracharya (Bhaskara II)He represented the peaks of mathematical knowledge in the 12th century and was the head of the astronomical observatory at Ujjain, the leading mathematical centre of ancient India.
#Bhaskara II’s family belonged to Deshastha Brahmin community, which served as court scholars at Kings forts. He learned Mathematics from his father Maheswara, an astrologer. He imparted his knowledge of mathematics to his son Lokasamudra, whose son had started a school to study the works of his grand father in 1207 AD.
His main work Siddhānta Shiromani, (Sanskrit for “Crown of treatises,“) is divided into four parts called Lilāvati(beautiful woman, named after his daughter Lilavati), Bijaganita, Grahaganita (mathematics of planets) and Golādhyāya (study of sphere/earth). These four sections deal with arithmetic, algebra, mathematics of the planets, and spheres respectively. He also wrote another treatise named Karna Kautoohala. Bhāskara’s work on calculus predates Newton and Leibniz by over half a millennium. He is particularly known in the discovery of the principles of differential calculus and its application to astronomical problems and computations.
While Newton and Leibniz have been credited with differential and integral calculus, there is strong evidence to suggest that Bhāskara was a pioneer in some of the principles of differential calculus. He was perhaps the first to conceive the differential coefficient and differential 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 thesame area in two different ways & then cancelling out two terms to get a2 + b2 = c2.
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.
Bhaskaracharya’s contributions to mathematics are very important, and a great pride for Indian, and a great gift to the world and civilization.
Herbert John