கணிதமேதை பாஸ்கராசார்யார்
செல்வன்
Bhaskara II or 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. Bhaskara was head of an astronomical observatory at Ujjain, the leading mathematical centre of ancient India. His predecessors in this post had included both the noted Indian mathematician Brahmagupta (598–c. 665) and Varahamihira. He lived in the Sahyadri region. It has been recorded that his great-great-great-grandfather held a hereditary post as a court scholar, as did his son and other descendants. His father Mahesvara was as an astrologer, who taught him mathematics, which he later passed on to his son Loksamudra. Loksamudra's son helped to set up a school in 1207 for the study of Bhāskara's writings
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| Bhaskara (1114 – 1185) (also known as Bhaskara II and Bhaskarachārya |
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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. Its translation in several languages of the world bear testimony to its eminence. 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 . His works fired the imagination of Persian and European scholars, who through research on his works earned fame and popularity.
A Summary of Bhaskara's contributions
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| Bhaskarachārya |
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- 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 (so-called "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. (See Calculus section below.)
- In Siddhanta Shiromani, Bhaskara developed spherical trigonometry along with a number of other trigonometric results. (See Trigonometry section below.)