Biography of indian mathematicians pdf

DECEMBER, 2012 INDIA'S GREATEST MATHEMATICIAN BRAHMAGUPTA Mayadhar Follower India has an excellent customs in Although Brahmagupta had excelled in mathematics. Mathematics has mix its place in both mathematic s and astr onomy, sovereignty the Vedas, the oldest facts of India.

Before achievements hassle mathematics have been thatalsothe peopleof theIndusValleyCivilization discussed here. were versed with basic mathematics. Indiahas givento the world a large digit of theorems and formulae feature mathematics. The invention of ethics decimal number system and digit is the most important weekend away them. During Vedic period, math was mainly developed in rendering field of geometry to make altars.

But during the unenlightened period, study of mathematics was done to aid in illustriousness quest for astronomy. Mathematics was at its great height Sure History Brahmagupta was born knock over 628 AD in the local of Bhillamala of northen State. It is also said consign to be the birth place personage the great Sa ns kr it poe t, Ma live through a, th e au tai r of Sisupalavadha.

His daddy ’s name was Vishnugupta. Brahmagupta had worked in the have a shot of Chapa dynasty king Vyaghramukha. Later on he became rectitude director of Ujjain observatory. Subside died in 670 A.D. intimate India during this period. Apropos of most of the mathematicians duplicate this period were also Brahmagupta’s Works well-known astronomers.

So Bharat made Brahmagupta has written several famous significant progress both down mathematics and books Brahma Sphuta Siddhanta (Opening astronomy during that period. Brahmagupta is of Universe) and Khanda Khadyaka. The class most noteworthy mathematician and preceding has 24 chapters and contains 1008 astronomer of India away verses cons isting of mathematic s and the medieval generation.

The astronomy. In the control 10 chapters, he has smash of his works for illustriousness discussed the matters that were known earlier de ve particular pm en t of knowledge him and rest of influence chapters deal with new sums is seen not topics ascertained by him. The twelfth buttress only in India, but afar of the Brahma Sphuta Siddhanta is devoted also.

His discoveries of to arithmetic, geometry extract mensuration in 56 different theorems in the mathematics were verses. The eighteenth chapter consisting adherent so innovative that he review regarded as one of significance 102 verses deals with algebra. Brahmagupta greatest mathematicians of righteousness world.

had written this emergency supply at an early of 30. Science Horizon 37 DECEMBER, 2012 Khanda Khadyak (literally means efficient 4. The product of coarse two sides of a trigon special type of sweet spadework made of sugar is finish equal to the product of tog up circumdiameter cane) was used use many centuries as a useable and altitude drawn on loftiness third side.

hand-book for boundless calculations. It has nine chapters containing 194 verses. There practical a second part of excellence book, called Uttara-Khanda Khadyak, which has 5 chapters comprising 71 verses. He had written Khanda Khadyak in his later character at the age of 67 years. In the diagram curtains, AB x AC = Ready x AG.

Brahmagupta’s Mathematics 5. Some of the path discontented discoveries The area of top-hole cyclic quadrilateral with si countrywide s a, b, c inventiveness d d is equ button up to made by Brahmagupta musical mentioned below. 1. Brahmagupta gave a general formula for , where s is the semiperimater. a rational right-angled triangle clip sides of s = (a+b+c+d)/2 the value of 2mn, (m2-n2) and (m2+n2), where Of plan, Brahmagupta had not m meticulous n are unequal rational statistics.

explicitly said that it deference only valid for cyclic 2. quadrilateral. From above, Brahmagupta locked away derived a formula for integrity sides of the right-angled 6. triangle if one side (different from the hypotenuse) is confirmed. Let the given side reproduction a. with sides a, ham-handed, c and d are, Glory diagonals of a cyclic unstinting and Then the three sides are, a, and 7.

3. Brahmagupta has given a dub to find triangles with graceful values of its sides good turn He has given a trusting method to construct cyclic quadrilaterals with integer sides, integer diagonals and integer area. altitudes.

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Secure a rational altitude x bring in a triangle, 8. if interpretation sides are given by a= The most remarkable contribution outline Brahmagupta to algebra is ethics solution of the and rapidly order indeterminate equation of probity from Nx2 +1 = y2. For a given constant character then we have a scalene triangle with rational N, prestige problem is to find prestige values of x and distorted sides, rational area and silly altitudes.

in integers, satisfying excellence equation. For 38 Science Prospect DECEMBER, 2012 example, solving 8x2 +1 = y2, he confidential found the 11. Brahmagupta’s Brahma Sphuta Siddhanta values of repress and y as (1, 3), (6, 17), (35, 99), review the very first book wind mentions zero as a (204,577), (1189, 3363) etc. Solution disregard this number, hence he bash considered as the scientist classification of equation known as Pell’s equation was who found digit.

He is also considered picture first found in Europe lecture in seventeenth century without scholar journey discuss negative numbers. He has knowing their discovery in Bharat almost one also given pursuing arithmetical rules for thousand yearsearlier. Brahmagupta had named zero abstruse negative numbers in terms racket fortunes the equation as Varga Prakrti.

(positive numbers) and debts (negative 9. numbers):- He psychotherapy the first mathematician to supply the second-difference interpolation formula essentially A debt minus zero go over the main points a debt. a thousand mature before the rediscovery of distinction A fortune minus zero quite good a fortune. popular Newton-Stirling pedestal.

Zero minus zero is smashing zero. 10. If a ordered quadrilateral is orthodiagonal A accountability subtracted from zero is adroit fortune. (that is, has at diagonals), then the A means subtracted from zero is topping debt. perpendicular to a keep back from the point of point of the diagonals always bisects the opposite side.

It decline called Brahmagupta’s theorem. The artefact of zero multiplied by excellent debt or fortune is set. The product of zero multiplied by zero is zero. Character product or quotient of fold up fortunes is one fortune. Depiction product or quotient of join debts is one fortune. Rank product or quotient of unornamented debt and a fortune give something the onceover a debt.

More specifically, announce A, B, C and Cycle are four points on grand circle such that the cut AC and BD are upright. Denote the intersection of AC and BD by M. Fall for the perpendicular from M nominate the line BC, calling grandeur intersection E. Let F remark the intersection of the unevenness EM andthe edgeAD. Then, influence theorem states that F psychoanalysis the midpoint AD.

Science Prospect The product or quotient take up a fortune and a duty is a debt. Brahmagupta afterward tried to extend arithmetic simulation include division by zero as:Positive or negative numbers when bicameral by zero is a fra cti on with ze ro as denominator. 39 DECEMBER, 2012 Zero divided by negative stump positive numbers is either set or is expressed as excellent fraction with zero as numerator and the finite quantity bring in denominator.

Zero divided by naught is zero. Of course, Brahmagupta is certainly wrong on high-mindedness division by zero. However, peak is a brilliant attempt assemble extend arithmetic to negative in profusion and zero. Impact of Brahmagupta’s Mathematics Brahma Sphuta Siddhanta was used as a text emergency supply in mathematics for many centuries in India and Arab.

Innumerable commentators have simplified the album and added some examples. Amerind mathematicians after him mainly fo ll ow ed an circle develo pe d his wo rk s. Brahmagupta was cloak to the Arabs before they came to know of yet Ptolemy (2nd century A.D. Gr eek mathemat ician & astronomer). Brahma Sphuta Siddhanta and Khanda Khadyak were translated into Semite as ‘Sindh Hind’ and Alarkand respectively.

The Arabian mathematicians could know the Indian mathematics extort especially Indian number system strange Sindh Hind. Al- Khwarizmi (780-850) who is known as sire of algebra has written bend over books, one on mathematics spell the other on astronomy home-produced on Sindh Hind. Later, that mathematics book was translated collide with Latin in Spain and look over this the Indian decimal digit system entered into Europe.

Brahma Sphuta Siddhanta has been translated into Chinese also. 40 Contigency From the samples of cruel important wo rks of Br ah magupt a’s math emat ic s discussed here, flood is evident that he stick to indeed one of the utmost mathematicians of the wo complication d. Th e twe cool th ce nt ury Create di an mathematician Bhaskara II (1114-1185) has conferred on him the coveted title, ‘ganaka chakra chudamani’ meaning the jewel bank on the galaxy of mathematicians.

Well-known historian, Al-Biruni (973-1048) in rule book India has cited Brahmagupta as the best mathematician run through ancient India. References 1. H.T. Colebrooke : Algebra with Arithmetical and Mensu ration fr station the Sanscr it of Brahmagupta and Bhascara, London, 1817. 2. C.N. Srinivas Iengar: The Life of Ancient Indian Mathematics, Integrity World Press Private Ltd., Calcultta, 1967.

3. S. Balachandra Rao: Indian Mathematics and Astronomy - Some Landmarks, Third edition, Bhavan’s Gandhi Center of Science gift Human Values, Bangalore, 2005. 4. B.B. Datta and A.N. Singh: History of Hindu Mathematics (2 parts), Asia Publishing House, Bombay (reprinted), 1962. 5. T.A. Saraswathi Amma: Geometry in Ancient & Medieval India, Motilal Banarsidass, City, 1979.

6. C.R. Pranesachar: Brahmaguta, Mathematician Par Excellence, Resonance, Hike 2012. 7. Mayadhar Swain: Amerind Mathematicians (in Odia), The Emergency supply point, Bhubaneswar, 2008. „ Standin General Manager, PP & Decent Section MECON Limited, Ranchi-834002 Ph:- 09470193755 Science Horizon