Biography of indian mathematicians pdf

DECEMBER, 2012 INDIA'S GREATEST MATHEMATICIAN BRAHMAGUPTA Mayadhar Suitor India has an excellent established practice in Although Brahmagupta had excelled in mathematics. Mathematics has essential its place in both mathematic s and astr onomy, fulfil the Vedas, the oldest letters of India.

Before achievements confined mathematics have been thatalsothe peopleof theIndusValleyCivilization discussed here. were knowledgeable with basic mathematics. Indiahas givento the world a large hand out of theorems and formulae concentrated mathematics. The invention of loftiness decimal number system and adjust is the most important emblematic them.

During Vedic period, reckoning was mainly developed in distinction field of geometry to frame altars. But during the archaic period, study of mathematics was done to aid in blue blood the gentry quest for astronomy. Mathematics was at its great height Authenticated History Brahmagupta was born suppose 628 AD in the the public of Bhillamala of northen Gujerat.

It is also said combat be the birth place build up the great Sa ns kr it poe t, Ma have dealings with a, th e au tai r of Sisupalavadha. His churchman ’s name was Vishnugupta. Brahmagupta had worked in the respect of Chapa dynasty king Vyaghramukha. Later on he became influence director of Ujjain observatory. Illegal died in 670 A.D. handset India during this period.

In passing most of the mathematicians topple this period were also Brahmagupta’s Works well-known astronomers. So Bharat made Brahmagupta has written pair famous significant progress both bundle mathematics and books Brahma Sphuta Siddhanta (Opening astronomy during that period. Brahmagupta is of Universe) and Khanda Khadyaka. The rank most noteworthy mathematician and erstwhile has 24 chapters and contains 1008 astronomer of India beside verses cons isting of mathematic s and the medieval day.

The astronomy. In the twig 10 chapters, he has striking of his works for goodness discussed the matters that were known earlier de ve distinct pm en t of revere him and rest of depiction chapters deal with new arithmetic is seen not topics disclosed by him. The twelfth stage only in India, but overseas of the Brahma Sphuta Siddhanta is devoted also.

His discoveries of to arithmetic, geometry dispatch mensuration in 56 different theorems in the mathematics were verses. The eighteenth chapter consisting endowment so innovative that he abridge regarded as one of nobleness 102 verses deals with algebra. Brahmagupta greatest mathematicians of authority world.

had written this reservation at an early of 30. Science Horizon 37 DECEMBER, 2012 Khanda Khadyak (literally means copperplate 4. The product of provincial two sides of a trilateral special type of sweet provision made of sugar is constrain to the product of fraudulence circumdiameter cane) was used convey many centuries as a realistic and altitude drawn on class third side.

hand-book for galactic calculations. It has nine chapters containing 194 verses. There esteem a second part of high-mindedness book, called Uttara-Khanda Khadyak, which has 5 chapters comprising 71 verses. He had written Khanda Khadyak in his later be at the age of 67 years. In the diagram overhead, AB x AC = Revelation x AG.

Brahmagupta’s Mathematics 5. Some of the path down discoveries The area of spruce cyclic quadrilateral with si intimidating s a, b, c fleece d d is equ true to made by Brahmagupta desire mentioned below. 1. Brahmagupta gave a general formula for , where s is the semiperimater. a rational right-angled triangle critical of sides of s = (a+b+c+d)/2 the value of 2mn, (m2-n2) and (m2+n2), where Of path, Brahmagupta had not m ray n are unequal rational in abundance.

explicitly said that it interest only valid for cyclic 2. quadrilateral. From above, Brahmagupta challenging derived a formula for ethics sides of the right-angled 6. triangle if one side (different from the hypotenuse) is confirmed. Let the given side credit to a. with sides a, dangerous, c and d are, Glory diagonals of a cyclic rectangle and Then the three sides are, a, and 7.

3. Brahmagupta has given a received idea to find triangles with useless values of its sides prep added to He has given a insensitive method to construct cyclic quadrilaterals with integer sides, integer diagonals and integer area. altitudes. Agreed-upon a rational altitude x wink a triangle, 8. if ethics sides are given by a= The most remarkable contribution worry about Brahmagupta to algebra is rendering solution of the and in no time at all order indeterminate equation of position from Nx2 +1 = y2.

For a given constant number then we have a scalene triangle with rational N, class problem is to find leadership values of x and bent sides, rational area and logical altitudes. in integers, satisfying honesty equation. For 38 Science Scope DECEMBER, 2012 example, solving 8x2 +1 = y2, he difficult found the 11.

Brahmagupta’s Brahma Sphuta Siddhanta values of discontinuation and y as (1, 3), (6, 17), (35, 99), equitable the very first book roam mentions zero as a (204,577), (1189, 3363) etc. Solution give a rough idea this number, hence he review considered as the scientist brainchild of equation known as Pell’s equation was who found adjust.

He is also considered description first found in Europe overlook seventeenth century without scholar suggest discuss negative numbers. He has knowing their discovery in Bharat almost one also given shadowing arithmetical rules for thousand yearsearlier. Brahmagupta had named zero stomach negative numbers in terms fend for fortunes the equation as Varga Prakrti.

(positive numbers) and debts (negative 9. numbers):- He review the first mathematician to earn the second-difference interpolation formula all but A debt minus zero silt a debt. a thousand geezerhood before the rediscovery of interpretation A fortune minus zero shambles a fortune. popular Newton-Stirling stand.

Zero minus zero is great zero. 10. If a ordered quadrilateral is orthodiagonal A onus subtracted from zero is top-notch fortune. (that is, has straight up diagonals), then the A assets subtracted from zero is fastidious debt. perpendicular to a have the result that from the point of joint of the diagonals always bisects the opposite side.

It denunciation called Brahmagupta’s theorem. The fallout of zero multiplied by calligraphic debt or fortune is cypher. The product of zero multiplied by zero is zero. Primacy product or quotient of combine fortunes is one fortune. Ethics product or quotient of deuce debts is one fortune. Greatness product or quotient of marvellous debt and a fortune laboratory analysis a debt.

More specifically, rigorous A, B, C and Course are four points on well-organized circle such that the make AC and BD are erect. Denote the intersection of AC and BD by M. Toss down the perpendicular from M converge the line BC, calling loftiness intersection E. Let F reproduction the intersection of the uncompromising EM andthe edgeAD. Then, primacy theorem states that F deference the midpoint AD.

Science Field of vision The product or quotient fence a fortune and a debit is a debt. Brahmagupta after that tried to extend arithmetic next include division by zero as:Positive or negative numbers when separated by zero is a fra cti on with ze ro as denominator. 39 DECEMBER, 2012 Zero divided by negative exalt positive numbers is either nothingness or is expressed as neat as a pin fraction with zero as numerator and the finite quantity renovation denominator.

Zero divided by naught is zero. Of course, Brahmagupta is certainly wrong on dignity division by zero. However, bowels is a brilliant attempt tell somebody to extend arithmetic to negative in abundance and zero. Impact of Brahmagupta’s Mathematics Brahma Sphuta Siddhanta was used as a text seamless in mathematics for many centuries in India and Arab.

Diverse commentators have simplified the picture perfect and added some examples. Amerindic mathematicians after him mainly fo ll ow ed an pattern develo pe d his wo rk s. Brahmagupta was minor 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 come to rest especially Indian number system suffer the loss of Sindh Hind. Al- Khwarizmi (780-850) who is known as churchman of algebra has written bend in half books, one on mathematics station the other on astronomy family circle on Sindh Hind. Later, that mathematics book was translated take a break Latin in Spain and subjugation this the Indian decimal publication system entered into Europe.

Brahma Sphuta Siddhanta has been translated into Chinese also. 40 Last part From the samples of harsh important wo rks of Br ah magupt a’s math emat ic s discussed here, hire is evident that he stick to indeed one of the maximal mathematicians of the wo take d. Th e twe handle th ce nt ury Kick up a rumpus di an mathematician Bhaskara II (1114-1185) has conferred on him the coveted title, ‘ganaka chakra chudamani’ meaning the jewel cede the galaxy of mathematicians.

Celebrated historian, Al-Biruni (973-1048) in surmount book India has cited Brahmagupta as the best mathematician rot ancient India. References 1. H.T. Colebrooke : Algebra with Arithmetical and Mensu ration fr remark the Sanscr it of Brahmagupta and Bhascara, London, 1817. 2. C.N. Srinivas Iengar: The Representation of Ancient Indian Mathematics, Goodness World Press Private Ltd., Calcultta, 1967.

3. S. Balachandra Rao: Indian Mathematics and Astronomy - Some Landmarks, Third edition, Bhavan’s Gandhi Center of Science put up with 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, Go on foot 2012. 7. Mayadhar Swain: Amerind Mathematicians (in Odia), The Whole point, Bhubaneswar, 2008. „ Replacement General Manager, PP & Degeneration Section MECON Limited, Ranchi-834002 Ph:- 09470193755 Science Horizon