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Mathematics

1. PADEGOGY OF MATHEMATICS Done by :- Ritesh Anand Section :- C Roll no.:- 221904 Topic :-contribution of Bhaskar in mathematics. ASSIGNED BY Mahendra mithrama

2. Introduction Baskara is also known as Bhaskara or Bhaskarcharya , this later name mean “ Baskara the teacher” He was born near Bijjada Biddha [ in present day called district Karnataka state] His father Mahesvara was the person who taught him about astronomy as he was Ujjain the leading mathematical center of ancient India. Bhaskara followed in his father’s footsteps and became a mathematician, astronomer and astrologer himself. He went on to become the head of an astronomical observatory at Ujjain, the leading mathematical centre of ancient India . The centre was a famous school of mathematical astronomy

3. Major contribution Area of Bhashkar in Mathematics Hindu Arabic Decimal System F irst degree of intermediate Equation T rigonometric formula . F irst discover gravity 500 years before Sir Issac Newton C alculations A rithematic W rite mathematics in poetic language Cardinal number P roof of the Pythagorean theorem D iscovered the principles of differential calculus and its application Quadratic equation In calculus Solutions of Diophantine Equations of the second order

4. Hindu Arabic Decimal System He was most likely the first to use a circle for the Zero for the Hindu Arabic Decimal System He is considered to be follower of aryabhatta and one of the most renowned scholars of the Aryabhatta’s astronical school Proof of the Pythagorean theorem He made many significant contributions to mathematics throughout his career . He is credited to have given a proof of the Pythagorean theorem by calculating the same area in two different ways and then canceling out terms to get a 2 + b 2 = c 2 . Quadratic equation In  Lilavati , solutions of quadric , cubic and quartic indeterminate equation are explained. Solutions of indeterminate quadratic equations (of the type  ax  +  b  =  y ).

5. He is credited to have discovered spherical trigonometry,a branch of spherical geometry which is of great importance for calculations in astronomy, geodesy and navigation. Trigonometric formula Algebra work ‘ Bijaganita ’ ("Algebra") was a work in 12 chapters. This book covered topics like positive and negative numbers, zero, surds, determining unknown quantities , and elaborated the method of ‘ Kuttaka ’ for solving indeterminate equations and Diophantine equations. He also filled many of the gaps in his predecessor Brahmagupta’s work. Calculations His work on calculus was groundbreaking and much ahead of his times. He not only discovered the principles of differential calculus and its application to astronomical problems and computations, but also determined solutions of linear and quadratic indeterminate equations ( Kuttaka ). The works in calculus performed by the Renaissance European mathematicians of the 17th century I s comparable to the rules he had discovered way back in the 12th century.

6. He wrote Siddantha siromani in 1500 A.D when he was 36 years old. It contains 1450 verses. It is divided into 4 parts Lilavathi Beejaganitha ("Algebra") Ganithadaya GolaDyaya In fact each part can be considered as separate Book. The number of verses in each part are as follows Lilavati has 278 verses Beejaganita has 213 verses, Ganitadhyaya has 451 Goladhyaya has 501 verses

7. Lilavati The first part ‘ Lilavati ’ consists of 13 chapters, mainly definitions, arithmetical terms, interest computation, arithmetical and geometrical progressions, plane geometry, and solid geometry among others. It also has a number of methods of computing numbers such as multiplications, squares, and progressions. Beejaganitha ("Algebra") His work ‘ Bijaganita ’ ("Algebra") was a work in 12 chapters. This book covered topics like positive and negative numbers, zero, surds , determining unknown quantities, and elaborated the method of ‘ Kuttaka ’ for solving indeterminate equations and Diophantine equations. He also filled many of the gaps in his predecessor Brahmagupta’s work.

8. The sections ‘ Ganitadhyaya ’ and ‘ Goladhyaya ’ of ‘ Siddhanta Shiromani’ are devoted to astronomy. He used an astronomical model developed by Brahmagupta to accurately define many astronomical quantities, including the length of the sidereal year. These sections covered topics such as mean longitudes of the planets, true longitudes of the planets, solar and lunar eclipses, cosmography and geography, etc. Ganithadaya and GolaDyaya

9. Baskara Tells “I have studied 8 books of Grammer 6 text of medicine, 6 books logic 5 books on bharat shastras , and 2 mimansas Conclusion