Bhaskaracharya

BHASKARACHARY A T H E G R E AT M AT H E M AT I T I A N

BHASKARACHAR YA

HIS LIFE HISTORY

ABOUT BHASKARACHARYA Bhaskarachārya was an Indian mathematician and astronomer who extended Brahmagupta's work on number systems. He was born near Bijjada Bida (in present day Bijapur district, Karnataka state, South India) into the Deshastha Brahmin family. He lived in the Sahyadri region. His father Mahesvara was as an astrologer, who taught him mathematics, which he later passed on to his son Loksamudra. Bhaskaracharya's work in Algebra, Arithmetic and Geometry catapulted him to fame and immortality. His renowned mathematical works called Lilavati" and Bijaganita are considered to be unparalleled and a memorial to his profound intelligence. In his treatise Siddhant Shiromani he writes on planetary positions, eclipses, cosmography, mathematical techniques and astronomical equipment. In the Surya Siddhant he makes a note on the force of gravity: "Objects fall on earth due to a force of attraction by the earth. Therefore, the earth, planets, constellations, moon, and sun are held in orbit due to this attraction." Bhaskaracharya was the first to discover gravity, 500 years before Sir Isaac Newton. He was the champion among mathematicians of ancient and medieval India .

BIRTH AND EDUCATION OF BHASKARACHARYA

 He was called ‘Ganakchakrachudamani’, which means, ‘a gem among all the

calculators of astronomical phenomena.’ Bhaskaracharya himself has written about his birth, his place of residence, his teacher and his education, in Siddhantashiromani as follows, ‘A place called ‘Vijjadveed’, which is surrounded by Sahyadri ranges, where there are scholars and all branches of knowledge are studied, a brahmin called Maheshwar was staying. I acquired knowledge at his feet’. He writes about his year of birth as follows, ‘I was born in Shake 1036 (1114 AD) and I wrote Siddhanta Shiromani when I was 36 years old.’Bhaskaracharya has also written about his education. Looking at the knowledge, which he acquired in a span of 36 years as follows‘I have studied eight books of grammar, six texts of medicine, six books on logic, five books of mathematics, four Vedas, five books on Bharat Shastras, and two Mimansas’. Bhaskaracharya calls himself a poet and most probably he was Vedanti, since he has mentioned ‘Parambrahman’ in that verse.

BHASKARACHARYA ‘S CONTRIBUTIONS  A proof of the Pythagorean theorem by calculating the same area in two different ways and then canceling out terms to get a² + b² = c².  In Lilavati, solutions of quadratic, cubic and quartic indeterminate equations.  Solutions of indeterminate quadratic equations (of the type ax² + b = y²).  Integer solutions of linear and quadratic indeterminate equations (Kuttaka). The rules he gives are (in effect) the same as those given by the Renaissance European mathematicians of the 17th century.  A cyclic Chakravala method for solving indeterminate equations of the form ax² + bx + c = y. The solution to this equation was traditionally attributed to William Brouncker in 1657, though his method was more difficult than the chakravala method.  His method for finding the solutions of the problem x² − ny² = 1 (socalled "Pell's equation") is of considerable interest and importance.  Solutions of Diophantine equations of the second order, such as 61x² + 1 = y². This very equation was posed as a problem in 1657 by the French mathematician Pierre de Fermat, but its solution was unknown in Europe until the time of Euler in the 18th century.

 Solved quadratic equations with more than one unknown, and found negative and irrational solutions.  Preliminary concept of mathematical analysis.  Preliminary concept of infinitesimal calculus, along with notable contributions towards integral calculus.  Conceived differential calculus, after discovering the derivative and differential coefficient.  Stated Rolle's theorem, a special case of one of the most important theorems in analysis, the mean value theorem. Traces of the general mean value theorem are also found in his works.  Calculated the derivatives of trigonometric functions and formulae.  In Siddhanta Shiromani, Bhaskara developed spherical trigonometry along with a number of other trigonometric results.

THE IDEA OF INFINITY

 He was the first to give that any no. divided by zero gives infinity.(∞)  He has written a lot about zero,surds,permutation and combination.  In mathematics, division by zero is division where the divisor (denominator) is  zero. Such a division can be formally expressed as a/0 where a is the dividend (numerator). In ordinary arithmetic, the expression has no meaning, as there is no number which, multiplied by 0, gives  a (assuming a≠0), and so division by zero is ∞.  Any number divided by 0= ∞  For example=> 9/0= ∞ 1025/0= ∞ 2048/0= ∞

Thank you Submitted byARNAV BARMAN CLASS-VIII F