02 DIVYAM.IKTP PRESENTATION ,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,

MAJOR POINTSOF IKTP TRIGNOATRY

1. SOTTHM Contribution Of Bharata In The Area Of Mathematics SUB Indian Traditional Knowledge & Practices (TTMITKP) Submitted By Divyam Sharma Submitted To Dr. Debasis Sahoo

2. Mathematics is found in scattered form – in sacred texts – the Samhitas, the Kalpasutras and the Vedangas. Information about enumeration, arithmetical opera-tions, fractions, properties of rectilinear figure, (present) Pythagoras’ theorem, surds, irrational numbers, quadratic and indeterminate equations, etc. is available in the Sulbasutras, which is the part of Kalpasutras. The Brahmanas and some sutras contain material about progressive series and permutations and combinations. In the classical period of Indian mathematics (400 CE to 1200 CE), important contributions were made by scholars like Aryabhatta, Brahmagupta, Bhaskara II, and Varāhamihira. INTRODUCTION

3. ARYABHATTA 476 CE - 550 CE Aryabhatta was one of the first major mathematician and astronomer from the classical age of the In d ian mathematics and also Indian astronomy. His main works are on the Aryabhatiya and the Arya-siddhanta.

4. Contribution In Mathematics Place V alue System A nd T he zero:

5. Contribution in the approximation of pi

6. Trigonometry Aryabhata gave a table of sines by the name ardha-jya, which means ‘half chord.

7. Cube roots and Square roots &

8. BAUDHAYANA (800BC - 740BC) The credit for authoring the earliest Sulba Sutras goes to him.The Sulbasutras is like a guide to the Vedas which formulate rules for constructing altars. In other words, they provide techniques to solve mathematical problems effortlessly . If a ritual was to be successful, then the altar had to conform to very precise measurements. It would not be incorrect to say that Baudhayana’s work on Mathematics was to ensure there would be no miscalculations in the religious rituals.

9. Circling a square Baudhayana was able to construct a circle almost equal in area to a square and vice versa. These procedures are described in his sutras (I-58 and I-59).

10. Baudhayana theorem Baudhāyana listed Pythagoras theorem in his book called Baudhāyana Śulbasûtra. .

11. BRAHMAGUPTA (590AD - 668AD) Brahmagupta was a great mathematician and astronomer. H e wrote many books on mathematics and astronomy. These include ‘Durkeamynarda’ (672), ‘Khandakhadyaka’ (665), ‘Brahmasphutasiddhanta’ (628) and ‘Cadamakela’ (624). The ‘Brahmasphutasiddhanta’ meaning the ‘Doctrine of Brahamagupta’ is one of his well-known works.

12. Properties of Zero When zero is added to a number or subtracted from a number, the number remains unchanged; and a number multiplied by zero becomes zero. A debt minus zero is a debt. A fortune minus zero is a fortune. Zero minus zero is a zero. A debt subtracted from zero is a fortune. A fortune subtracted from zero is a debt. The product of zero multiplied by a debt or fortune is zero. The product of zero multiplied by zero is zero.

13. Sum of Series He gave the sum of, a series of cubes and a series of squares for the first n natural numbers as follows: 1² + 2² +…….+n² = (n)(n+1)(2n+1)⁄6 1³ + 2³ +…….+n³ = (n(n+1)⁄2)² Interpolation formula sphuta-bhogyakhanda = (Dr + Dr-1)⁄2 ± t|Dr – Dr-1|⁄2, where ± is introduced according to Dr < Dr+1 or Dr > Dr+1 and f(a) is given by, f(a) = fr + t × sphuta-bhogyakhanda, is known as Stirling’s interpolation formula for second-order differences.

14. Brahmagupta’s Formula The approximate area is the product of the halves of the sums of the sides and opposite sides of a triangle and a quadrilateral. The accurate area is the square root from the product of the halves of the sums of the sides diminished by each side of the quadrilateral.

15. Brahmagupta Theorem If a cyclic quadrilateral is orthodiagonal (i.e., has perpendicular diagonals), then the perpendicular to a side from the point of intersection of the diagonals always bisects the opposite side.

16. Bhaskara I (600AD - 680AD) He was most likely the first to use a circle for the zero in the Hindu-Arabic decimal system N umbers and S ymbolism . T he names and solution of the first degree equations . Q uadratic equations, C ubic equations and equations which have more than one unknown value . S ymbolic algebra & the algorithm method to solve linear indeterminate equations .

17. Bhaskara II (1114AD - 1185AD) Lilavati - It covers calculations, progressions, measurement, permutations. Bijaganita - It discusses zero, infinity, positive and negative numbers, and indeterminate equations including (the now called) Pell's equation. Grahaganita - While treating the motion of planets, he considered their instantaneous speeds. T he Siddhānta-Śiromani

18. Mādhava of Sangamagrāma (c. 1340 – c. 1425) Infinite series Trigonometry

19. Thank you for listening