Presentation on famous mathematicians in india

FAMOUS MATHEMATICIANS IN INDIA

1. FAMOUS MATHEMATICIANS IN INDIA

2. ARYABHATA

3. Aryabhata was the first of the major mathematician-astronomers from the classical age of Indian mathematics and Indian astronomy.His work include the Aryabhatiya and thebAryasiddhanta. Numerical values: He made a notation system in which Digits are denoted with the help of alphabet numerals. Notation system: He invented a notation system consisting of alphabet numerals.Digits were denoted by alphabet numeral Place value: Aryabhatta was familiar with the place value sysyem. He knew numerical symbols and the sign for zero. Square toot and cube root: His calculayions on square root and cube root would not have been possible without the knowledge of place values system and zero.He has given methods ofbextracting square root cube root along with their explanation. Interest: He formulated for the first time in India the formula for interest , time and other related ones, in the problems of interest.

4. Trigonometry : He gave the area of a triangle as: tribhujasya phalashariram samadalakoti bhujardhasamvargah that translates to: "for a triangle, the result of a perpendicular with the half-side is the area." He also discussed the concept of sine in his work by the name of ardha-jya, which literally means "half-chord".   Algebra: In Aryabhatiya, he provided elegant results for the summation of series of squares and cubes:

5. 2 SRINIVASA RAMANUJAN

6. Srinivasa Ramanujan  was one of India's greatest mathematical geniuses. He made substantial contributions to the analytical theory of numbers and worked on  elliptic functions ,  continued fractions , and infinite series. (1) Aryabhatta was born in 476 A.D. Kusumpur, India.He was the first in the line of great mathematicians from the classical age of Indian Mathematics and Astrono (2) His famous work are the” Aryabhatiya “and the”Arya‐siddhanta”.The Mathematical part of the Aryabhatiya covers arithmetic. algebra, plane and spherical trigonometry.The Arya‐siddhanta, a lot work on astronomical computation. (3) Approximation of Pi: Aryabhata work on the approximation for pi ( π) and may have come to the conclusion that  π  is an irrational number.In the 2nd part of Aryabhatiya, he writes the ratio of circumference to diameter is 3.1416. (4) Aryabhata given the formula for area of a triangle .He also discussed the concept of sine in his work by the name of ardhajya. If we use Aryabhata’s table & calculate the value of sin300 which is 1719/3438=0.5.,the value is correct. His alphabetic code is commonly known as the Aryabhata cipher.   (5) He was first person to say that Earth is spherical and it revolves around the sun.

7. (6) He gave the formula (a+b)2 =a2 + b2 + 2ab. (7) He taught the method of solving the following problems: 1+2+3+…………+n = n(n+1)/2 12 + 22 + 32 +………+ n2 = n(n+1)(2n+1)/6 13 + 23 + 33 +…………..+ n3 = (n(n+1)/2)2

8. BRAHMAGUPTA

9. (1) Brahmagupta was born in 598 A.D.in Bhinmal city in the state of Rajasthan. He was a mathematician and astronomer, who wrote many important works on mathematics and astronomy. His best known work is the “Brahmasphuta‐siddhanta”, written in 628 AD in Bhinmal. (2) He was the first to use zero as a number. He gave rules to compute with zero. (3) He gave four methods of multiplication. (4) He gave following formulae, used in G.P. series a+ar+ar2 +ar3 +……….+arn‐1 =a(rn  ‐1)/( r‐1) (5) He gave the following formulae(Brahmagupta’s formula): Area of a cyclic quadrilateral with side a,b,c,d =9(s‐a)(s‐b)(s‐c)(s‐d), where 2s= a+b+c+d.

10. 4 BHASKARACHARYA

11. (1) He was born in Bijapur in modern Karnataka. He & his work represent a significant contribution to mathematical & astronomical knowledge in the 12th century. (2) His main work “Siddhanta Shiromani” is divided into four parts called Lilawati, Bijaganit, Grahaganita and Goladhyaya. These four sections deal with arithmetic, algebra, mathematics of planets and spheres respectively. (3) He was the first to give that any number divided by zero gives infinity. (4) He was written a lot about zero, surds, permutation and combination. (5) He wrote,” The hundredth part of the circumference of a circle seems to be straight. Our earth is a big sphere and that’s why it appears to be flat.” (6) He gave the formulae like: sin(A±B)=sinAcosB ±  cosA sinB. (7) He calculated derivatives of Trigonometric functions and formulae. (8) He developed spherical trigonometry alongwith a number of other trigonometric results. (9) He explained solution of quadratic, cubic and quartic indeterminate equations. (10) He developed a proof of Pythagoras Theorem by calculating the same area in two different ways & these cancel out terms to get a2 + b2 = c 2. (11) He gave first general method for finding the solution of the problem x 2 – ny2 = 1 (so called Pell’s equation ). (12) He gave solution of Diophantine equations of second order such as 61x2 + 1 = y 2..

12. 5 SHAKUNTALA DEVI

13. (1) She was born in 1939.She is an Indian calculating prodigy. (2) By age 6,She demonstrated her calculation and memorization abilities at university of Mysore. At the age of 8,she had successes at Annamalai University by doing the same. (3) On June 18, 1980,She demonstrated the multiplication of two 13‐digit numbers 7,686,369,774,870X2,465,099.745,779 picked at random by the Computer Department of Imperial College, London. She answered the question in 28 seconds. However,the time is more likely the time for dictating the answer (a 26‐digit number) than the time for mental calculation(the time of 28 seconds was quoted on her website).Her answer was 18,947,668,177,995,426,773,730.This event is mentioned on page 26 of the 1995 Guinness Book of Records (4) In Dallas, she competed with a computer to see who give the cube of 188138517 faster, she won. At University of USA she was asked to give the 23rd root of 91674867692003915809866092758538016248310668014430862240712651642793465 70408670965932792057674808067900227830163549248523803357453169351119035 9657754734007568818688305620821016129132845564895780158806771. She answered in 50 seconds. The answer is 546372891.It took a UNIVAC 1108 computer, full one minute (10 seconds more) to confirm that she was right after it was fed with 13000 instructions. (5) Now she is known to be Human Computer.

14. 6 P .C . MAHALANOBIS

15. Prasanta Chandra Mahalanobis(29 June 1893- 28 June 1972) Was an Indian scientist and applied statistician.He is best remembered for the Mahalanobis distance, a statistical measure.He made pioneering studies in anthropometrh in India.He founded the Indian statistical Institute,and contributed to the design of large- scale sample surveys. MAHALANOBIS DISTANCE The Mahalanobis distance is a descriptive statistic that provides a relative measure of a data point’s distance (residual) from a commom point.It is a unitless measure introduced by P.C .M ahalanobis in 1936 .The Mahalanobis distance is used to identify and guagebsimilarity of an unknown sample set to a known one.It differs from Euclidean distance in that it takes into account the correlations of the data set and is scale- invariant. In other words,it has a multivariate effect size

16. 7 C . R . RAO

17. Calyampudi Radhakrishna Rao , FRS known as  C R Rao  (born 10 September 1920) is an Indian-born,  naturalised  American, mathematician and statistician. He is currently  professor emeritus  at Penn State University and Research Professor at the  University at Buffalo. Rao has been honoured by numerous colloquia, honorary degrees, and  festschrifts  and was awarded the US  National Medal of Science  in 2002.The  American Statistical Association has described him as "a living legend whose work has influenced not just statistics, but has had far reaching implications for fields as varied as economics, genetics, anthropology, geology, national planning, demography, biometry, and medicine."  The Times of India  listed Rao as one of the top 10 Indian scientists of all time. Rao is also a Senior Policy and Statistics advisor for the  Indian Heart Association non-profit focused on raising South Asian cardiovascular disease awareness Among his best-known discoveries are the  Cramér–Rao bound and the  Rao–Blackwell theorem both related to the quality of  estimators . Other areas he worked in include  multivariate analysis ,  estimation theory , and  differential geometry . His other contributions include the Fisher–Rao Theorem, Rao distance, and orthogonal arrays. He is the author of 14 books and has published over 400 journal publications.

18. He was the President of the  International Statistical Institute , Institute of Mathematical Statistics (USA), and the  International Biometric Societ. He was inducted into the Hall of Fame of India's National Institution for Quality and Reliability (Chennai Branch) for his contribution to industrial statistics and the promotion of quality control programs in industries. The  Journal of Quantitative Economics  published a special issue in Rao's honour in 1991. "Dr Rao is a very distinguished scientist and a highly eminent statistician of our time. His contributions to statistical theory and applications are well known, and many of his results, which bear his name, are included in the curriculum of courses in statistics at bachelor's and master's level all over the world. He is an inspiring teacher and has guided the research work of numerous students in all areas of statistics. His early work had greatly influenced the course of statistical research during the last four decades. One of the purposes of this special issue is to recognise Dr Rao's own contributions to econometrics and acknowledge his major role in the development of econometric research in India." In his honour The  Pennsylvania State University  has established C. R. and Bhargavi Rao Prize in Statistics, CR Rao Advanced Institute of Mathematics, Statistics and Computer Science National Award in Statistics established by  Ministry of Statistics and Programme Implementation  (MoSPI), Government of India. The road from  IIIT Hyderabad  passing along  Central University of Hyderabad  crossroads to Alind Factory,  Lingampally is named as "Prof. C.R. Rao Road"

19. 8 MAHAVIRA

20. Mahavira was a 9 th century Indian mathematician from Gulbarga who asserted that the square root of a negative number did not exist.He gave the sum of a series of whose terms are squares of an arithmetical progression and empirical rules for area and perimeter of an ellipse .He was patronised by the great Rashtrakuta king Amoghavarsha.Mahavira was the author of Ganit Saar Sangraha.He seperated Astology from Mathematics.He expounded on the same subjects on which Aryabhata and Brahmagupta contended,but he expressed them more clearly.He is highly respected among Indian Mathematicians,because of his establishment of terminology for concepts such as equilateral,and isosceles triangle,rhombus,circle and semicircle .Mahaviras eminence spred in all South India and his books proved inspirational yo other Mathematicians in Southern India

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