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Great mathematician


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Great mathematician

Great mathematician

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  • 1. A Project Report on Great Mathematicians Submmited by - Rajat Anand Ph no. 8439735931
  • 2. Index
    • Aryabhatta
    • Srinivasa Ramanujam
    • Bhaskaracharya
    • Shakuntala Devi
    • Brahmagupta
    • Narayana Pandit
  • 3. Aryabhatta Aryabhatta came to this world on the 476 A.D at Patliputra in Magadha which is known as the modern Patna in Bihar. Some people were saying that he was born in the South of India mostly Kerala. But it cannot be disproved that he was not born in Patlipura and then travelled to Magadha where he was educated and established a coaching centre. His first name is “Arya” which is a South Indian name and “Bhatt” or “Bhatta” a normal north Indian name which could be seen among the trader people in India. No matter where he could be originated from, people cannot dispute that he resided in Patliputra because he wrote one of his popular “Aryabhatta-siddhanta” but “Aryabhatiya” was much more popular than the former. Aryabhatta do for his survival. His writing consists of mathematical theory and astronomical theory which was viewed to be perfect in modern mathematics. For example, it was written in his theory that when you add 4 to 100 and multiply the result with 8, then add the answer to 62,000 and divide it by 20000, the result will be the same thing as the circumference with diameter twenty thousand. The calculation of 3.1416 is nearly the same with the true value of Pi which is 3.14159. Aryabhatta’s strongest contribution was zero. Another aspect of mathematics that he worked upon is arithmetic, algebra, quadratic equations, trigonometry and sine table.
  • 4.
    • Aryabhatta was aware that the earth rotates on its axis. The earth rotates round the sun and the moon moves round the earth. He discovered the 9 planets position and related them to their rotation round the sun. Aryabhatta said the light received from planets and the moon is gotten from sun. He also made mention on the eclipse of the sun, moon, day and night, earth contours and the 365 days of the year as the exact length of the year. Aryabhatta also revealed that the earth circumference is 24835 miles when compared to the modern day calculation which is 24900 miles.
    • Aryabhatta have unusually great intelligence and well skilled in the sense that all his theories has became wonders to some mathematicians of the present age. The Greeks and the Arabs developed some of his works to suit their present demands. Aryabhatta was the first inventor of the earth sphericity and also discovered that earth rotates round the sun. He was the one that created the formula (a + b)2 = a2 + b2 + 2ab
  • 5. Srinivasa Ramanujam
    • Ramanujam was born on December 27, 1887, in Erode.
    • He was a very great and famous mathematician.
    • He made contributions to the analytical theory of numbers.
    • His father worked in Kumbakonam as a clerk in a cloth merchant's shop.
    • When he was nearly five years old, Ramanuja m entered the primary school .
  • 6.
    • Ramanujan was appointed to the post of clerk and began his duties on 1 March 1912.
    • Ramanujan was quite lucky to have a number of people working round him with training in mathematics.
    • He died on 26 th April 1920 in Kumbakonam.
    • Ramanujan continued to develop his mathematical ideas and began to pose problems and solve problems in the Journal of the Indian Mathematical Society.
    • He developed relations between elliptic modular equations in 1910.
    • In 1912 Ramanujan applied for the post of clerk in the accounts section of the Madras Port Trust.
  • 7. Bhaskaracharya
    • Bhaskaracharya otherwise known as Bhaskara is probably the most well known mathematician of ancient Indian today. Bhaskara was born in 1114 A.D. according to a statement he recorded in one of his own works. He was from Bijjada Bida near the Sahyadri mountains. Bijjada Bida is thought to be present day Bijapur in Mysore state. Bhaskara wrote his famous Siddhanta Siroman in the year 1150 A.D. It is divided into four parts; Lilavati (arithmetic), Bijaganita (algebra), Goladhyaya (celestial globe), and Grahaganita (mathematics of the planets). Much of Bhaskara's work in the Lilavati and Bijaganita was derived from earlier mathematicians; hence it is not surprising that Bhaskara is best in dealing with indeterminate analysis. In connection with the Pell equation, x^2=1+61y^2, nearly solved by Brahmagupta, Bhaskara gave a method (Chakravala process) for solving the equation.
    • O girl! out of a group of swans, 7/2 times the square root of the number are playing on the shore of a tank. The two remaining ones are playing with amorous fight, in the water. What is the total number of swans?
    • Teaching and learning mathematics was in Bhaskara's blood. He learnt mathematics from his father, a mathematician, and he himself passed his knowledge to his son Loksamudra. To return to the timeline click here: timeline.
  • 8.
    • A very great mathematician and an astronomer of the Kaliyuga's 43rd century ( i.e. 12th century A.D ) Bhaskaracharya was the head of the observatory at Ujjain. There are two famous works of his on Mathematical Astronomy - Siddhanta-Siromani and Karana-Kutuhala. Besides his work on Algebra, Lilavati Bija Ganita too is famous. The law of Gravitation, in clear tems, had been propounded by Bhaskaracharya 500 years before it was rediscovered by Newton. Centuries before him there had been another mathematician Bhaskaracharya also in Bharat ( India ).
    • The subjects of his six works include arithmetic, algebra, trigonometry, calculus, geometry, astronomy. There is a seventh book attributed to him which is thought to be a forgery. Bhaskaracharya discovered the concept of differentials, and contributed a greater understanding of number systems and advanced methods of equation solving. He was able to accurately calculate the sidreal year, or the time it takes for the earth to orbit the sun. There is but a scant difference in his figure of 365.2588 days and the modern figure of 365.2596 days.
  • 9.
    • Shakuntala Devi is a calculating prodigy who was born on November 4, 1939 in Bangalore, India. Her father worked in a "Brahmin circus" as a trapeze and tightrope performer, and later as a lion tamer and a human cannonball. Her calculating gifts first demonstrated themselves while she was doing card tricks with her father when she was three. They report she "beat" them by memorization of cards rather than by sleight of hand. By age six she demonstrated her calculation and memorization abilities at the University of Mysore. At the age of eight she had success at Annamalai University by doing the same. Unlike many other calculating prodigies, for example Truman Henry Safford, her abilities did not wane in adulthood. In 1977 she extracted the 23rd root of a 201-digit number mentally. On June 18, 1980 she demonstrated the multiplication of two 13-digit numbers 7,686,369,774,870 x 2,465,099,745,779 picked at random by the Computer Department of Imperial College, London. She answered the question in 28 seconds. However, this time is more likely the time for dictating the answer (a 26-digit number) than the time for the mental calculation (the time of 28 seconds was quoted on her own website). Her correct answer was 18,947,668,177,995,426,462,773,730.
    Shakuntala Devi
  • 10.
    • This event is mentioned on page 26 of the 1995 Guinness Book of Records ISBN 0-553-56942-2. In 1977, she published the first study of homosexuality in India.According to Subhash Chandra's review of Ana Garcia-Arroyo's book The Construction of Queer Culture in India: Pioneers and Landmarks,For Garcia-Arroyo the beginning of the debate on homosexuality in the twentieth century is made with Shakuntala Devi's book The World of Homosexuals published in 1977. [...] Shakuntala Devi's (the famous mathematician) book appeared. This book went almost unnoticed, and did not contribute to queer discourse or movement. [...] The reason for this book not making its mark was becauseShakuntala Devi was famous for her mathematical wizardry and nothing of substantial import in the field of homosexuality was expected from her. Another factor for the indifference meted out to the book could perhaps be a calculated silence because the cultural situation in India was inhospitable for an open and elaborate discussion on this issue. In 2006 she has released a new book called In the Wonderland of Numbers with Orient Paperbacks which talks about a girl Neha and her fascination for numbers.
  • 11. Brahmagupta
    • Brahmagupta, whose father was Jisnugupta, wrote important works on mathematics and astronomy. In particular he wrote  Brahmasphutasiddhanta  (The Opening of the Universe), in 628. The work was written in 25 chapters and Brahmagupta tells us in the text that he wrote it at Bhillamala which today is the city of Bhinmal. This was the capital of the lands ruled by the Gurjara dynasty.
    • Brahmagupta became the head of the astronomical observatory at Ujjain which was the foremost mathematical centre of ancient India at this time. Outstanding mathematicians such as  Varahamihira  had worked there and built up a strong school of mathematical astronomy.
    • In addition to the  Brahmasphutasiddhanta  Brahmagupta wrote a second work on mathematics and astronomy which is the  Khandakhadyaka  written in 665 when he was 67 years old. We look below at some of the remarkable ideas which Brahmagupta's two treatises contain. First let us give an overview of their contents.
  • 12.
    • The  Brahmasphutasiddhanta  contains twenty-five chapters but the first ten of these chapters seem to form what many historians believe was a first version of Brahmagupta's work and some manuscripts exist which contain only these chapters. These ten chapters are arranged in topics which are typical of Indian mathematical astronomy texts of the period. The topics covered are: mean longitudes of the planets; true longitudes of the planets; the three problems of diurnal rotation; lunar eclipses; solar eclipses; risings and settings; the moon's crescent; the moon's shadow; conjunctions of the planets with each other; and conjunctions of the planets with the fixed stars.
    • The remaining fifteen chapters seem to form a second work which is major addendum to the original treatise. The chapters are: examination of previous treatises on astronomy; on mathematics; additions to chapter 1; additions to chapter 2; additions to chapter 3; additions to chapter 4 and 5; additions to chapter 7; on algebra; on the gnomon; on meters; on the sphere; on instruments; summary of contents; versified tables
  • 13. Narayana Pandit
    • Narayana was the son of Nrsimha (sometimes written Narasimha). We know that he wrote his most famous work  Ganita Kaumudi  on arithmetic in 1356 but little else is known of him. His mathematical writings show that he was strongly influenced by  Bhaskara II  and he wrote a commentary on the  Lilavati  of  Bhaskara II called  Karmapradipika.  Some historians dispute that Narayana is the author of this commentary which they attribute to  Madhava .
    • In the  Ganita Kaumudi  Narayana considers the mathematical operation on numbers. Like many other Indian writers of arithmetics before him he considered an algorithm for multiplying numbers and he then looked at the special case of squaring numbers. One of the unusual features of Narayana's work  Karmapradipika  is that he gave seven methods of squaring numbers which are not found in the work of other Indian mathematicians.
    • He discussed another standard topic for Indian mathematicians namely that of finding triangles whose sides had integral values. In particular he gave a rule of finding integral triangles whose sides differ by one unit of length and which contain a pair of right-angled triangles having integral sides with a common integral height. In terms of geometry Narayana gave a rule for a segment of a circle. Narayana
  • 14.
    • Narayana also gave a rule to calculate approximate values of a square root. He did this by using an indeterminate equation of the second order,  Nx 2 + 1 =  y 2, where N  is the number whose square root is to be calculated. If  x  and  y  are a pair of roots of this equation with  x  <  y  then √ N  is approximately equal to  y / x . To illustrate this method Narayana takes  N  = 10. He then finds the solutions  x  = 6,  y  = 19 which give the approximation 19/6 = 3.1666666666666666667, which is correct to 2 decimal places. Narayana then gives the solutions  x  = 228,  y  = 721 which give the approximation 721/228 = 3.1622807017543859649, correct to four places. Finally Narayana gives the pair of solutions  x  = 8658,  y  = 227379 which give the approximation 227379/8658 = 3.1622776622776622777, correct to eight decimal places. Note for comparison that √10 is, correct to 20 places, 3.1622776601683793320
  • 15.