7 contributionsof indian mathematicians to mathematics

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1. CONTRIBUTION OF MATHEMATICIAN TO MATHEMATICS NATURE OF MATHEMATICS OBJECTIVE OF MATHEMATICS CHRACTERISTICS OF MATHEMATICS MATHEMATICS AND PHYSICAL WORLD HISTORY OF MATHEMATICS USEFUL FOR TEACHER CONTRIBUTION OF INDIAN MATHEMATICIAN CONCLUSION BIBLIOGRAPHY

2. NATURE OF MATHEMATICS Is a science of number and space. Own language-signs, symbols, terms and operations. Involves man’s high cognitive powers. Has own tools like intuition, logic, reasoning, analysis, etc. Helps in drawing conclusions and interpreting various ideas. The tool specially suited for dealing with abstract ideas. It helps in solving the problems of our life.

3. OBJECTIVE OF MATHEMATICS Knowledge and understanding objectives. Skill objectives. Application objectives. Attitude objectives. Appreciation and interest objectives.

4. CHARACTERISTICS OF MATHEMATICS It is the science of measurement, quantity and magnitude. It is the systematized, organized and extract branch of science. It is the science of calculations. It deals with quantitative facts and relationships. It is the abstract form of science. It is a science of logical reasoning. It is an inductive and experimental science.

5. MATHEMATICS AND THE PHYSICAL WORLD If we take physics we see that its study requires the knowledge of mathematics at every point. All the physical laws, laws of motion, laws of lever, etc can only be understood and applied with the help of the understanding of mathematics. The need of the numerical calculations in dealing with the problems in physics clearly reveals the value of mathematics in learning physics.

6. HISTORY OF MATHEMATICS USEFUL FOR TEACHER Role of mathematics in various walks of life. Shows the correlation of mathematics. Brings out significant developments. Makes mathematics teaching effective. Easier to understand. Helps in gradation. Helps in enhancing the reputation. Better understanding of the subject.

7. CONTRIBUTION OF MATHEMATICIANS TO MATHEMATICS RAMANUJAN He was born on 22 na of December 1887 in a small village of  Tanjore district, Madras.He failed in English in Intermediate, so his formal studies were stopped but his self-study of mathematics continued. He sent a set of 120 theorems to Professor Hardy of Cambridge. As a result he invited Ramanujan to England. Ramanujan showed that any big number can be written as sum of not more than four prime numbers. He showed that how to divide the number into two or more squares or cubes.

8. CONTRIBUTION OF MATHEMATICIANS TO MATHEMATICS ARYABHATTA Aryabhatta was born in 476A.D in Kusumpur , India. He was the first person to say that Earth is spherical and it revolves around the sun. He gave the formula (a + b) 2 = a 2 + b 2 + 2ab He taught the method of solving the following problems: 1 4 + 2 4 + 3 4 + 4 4 + 5 4 + …………+ n4 = n(n+1) (2n+1) (3n 2 +3n-1)/30

9. CONTRIBUTION OF MATHEMATICIANS TO MATHEMATICS BRAHMA GUPTA Brahma Gupta was born in 598A.D in Pakistan. He gave four methods of multiplication. He gave the following formula, used in G.P series a + ar + ar 2 + ar 3 +……….. + ar n-1 = (ar n-1 ) ÷ (r – 1) He gave the following formulae : Area of a cyclic quadrilateral with side a, b, c, d= √(s -a)(s- b)(s -c)(s- d) where 2s = a + b + c + d

10. CONTRIBUTION OF MATHEMATICIANS TO MATHEMATICS SHAKUNTALA DEVI She was born in 1939 In 1980, she gave the product of two, thirteen digit numbers within 28 seconds, many countries have invited her to demonstrate her extraordinary talent. In Dallas she competed with a computer to see who give the cube root of 188138517 faster, she won. At university of USA she was asked to give the 23 rd root of9167486769200391580986609275853801624831066801443086224071265164279346570408670965932792057674808067900227830163549248523803357453169351119035965775473400756818688305620821016129132845564895780158806771.She answered in 50seconds. 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. Now she is known to be Human Computer.

11. CONTRIBUTION OF MATHEMATICIANS TO MATHEMATICS BHASKARACHARYA He was born in a village of Mysore district. He was the first to give that any number divided by 0 gives infinity (00). He has written a lot about zero, surds, permutation and combination. 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.” He gave the formulae like sin(A ± B) = sinA.cosB ± cosA.sinB

12. CONTRIBUTION OF MATHEMATICIANS TO MATHEMATICS MAHAVIRA Mahavira was a 9th-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 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 separated Astrology 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. Mahavira’s eminence spread in all South India and his books proved inspirational to other Mathematicians in Southern India.

13. CONTRIBUTION OF MATHEMATICIANS TO MATHEMATICS PYTHAGORAS This eventually led to the famous saying that “all things are numbers.” Pythagoras himself spoke of square numbers and cubic numbers, and we still use these terms, but he also spoke of oblong, triangular, and spherical numbers. He associated numbers with form, relating arithmetic to geometry. His greatest contribution, the proposition about right-angled triangles, sprang from this line of thought: From Pythagoras we observe that an answer to a problem in science may give raise to new questions. For each door we open, we find another closed door behind it. Eventually these doors will be also be opened and reveal answers in a new dimension of thought. A sprawling tree of progressively complex knowledge evolves in such manner. This Hegelian recursion, which is in fact a characteristic of scientific thought, may or may not have been obvious to Pythagoras. In either way he stands at the beginning of it.

14. CONTRIBUTION OF MATHEMATICIANS TO MATHEMATICS ARYABHATTA I Quadratic equations Trigonometry The value of π , correct to 4 decimal places. Arithmetic Algebra Mathematical astronomy Calculus

15. CONTRIBUTION OF MATHEMATICIANS TO MATHEMATICS VARAHAMIHIRA Varahamihira (505-587) produced the Pancha Siddhanta ( The Five Astronomical Canons ). He made important contributions to trigonometry , including sine and cosine tables to 4 decimal places of accuracy and the following formulas relating sine and cosine functions: sin 2 ( x ) + cos 2 ( x ) = 1

16. CONTRIBUTION OF MATHEMATICIANS TO MATHEMATICS NIELS HENRIK ABEL Niels Henrik Abel (August 5, 1802 – April 6, 1829) was a noted Norwegian mathematician [1] who proved the impossibility of solving the quintic equation in radicals.

17. CONTRIBUTION OF MATHEMATICIANS TO MATHEMATICS CARL FRIEDRICH GAUSS Johann Carl Friedrich Gauss (30 April 1777 – 23 February 1855) was a German mathematician and scientist who contributed significantly to many fields, including number theory , statistics , analysis , differential geometry , geodesy , geophysics , electrostatics , astronomy and optics . Sometimes known as the Princeps mathematicorum and “greatest mathematician since antiquity”, Gauss had a remarkable influence in many fields of mathematics and science and is ranked as one of history’s most influential mathematicians. He referred to mathematics as “the queen of sciences.” He completed Disquisitiones Arithmeticae , his magnum opus , in 1798 at the age of 21, though it would not be published until 1801. This work was fundamental in consolidating number theory as a discipline and has shaped the field to the present day.

18. CONTRIBUTION OF MATHEMATICIANS TO MATHEMATICS LEONHARD EULER Leonhard Paul Euler (15 April 1707 – 18 September 1783) was a pioneering Swiss mathematician and physicist who spent most of his life in Russia and Germany . Euler made important discoveries in fields as diverse as infinitesimal calculus and graph theory . He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis , such as the notion of a mathematical function . He is also renowned for his work in mechanics , fluid dynamics , optics , and astronomy . Euler is considered to be the preeminent mathematician of the 18th century and one of the greatest of all time. He is also one of the most prolific; his collected works fill 60–80 quarto volumes. A statement attributed to Pierre-Simon Laplace expresses Euler’s influence on mathematics: “Read Euler, read Euler, he is the master [i.e., teacher] of us all.” Euler was featured on the sixth series of the Swiss 10- franc banknote and on numerous Swiss, German, and Russian postage stamps . The asteroid 2002 Euler was named in his honor. He is also commemorated by the Lutheran Church on their Calendar of Saints on 24 May – he was a devout Christian (and believer in biblical inerrancy ) who wrote apologetics and argued forcefully against the prominent atheists of his time.

19. CONTRIBUTION OF MATHEMATICIANS TO MATHEMATICS DAVID HILBERT David Hilbert (January 23, 1862 – February 14, 1943) was a German mathematician , recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. He discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of geometry . He also formulated the theory of Hilbert spaces one of the foundations of functional analysis . Hilbert adopted and warmly defended Georg Cantor ‘s set theory and transfinite numbers . A famous example of his leadership in mathematics is his 1900 presentation of a collection of problems that set the course for much of the mathematical research of the 20th century. Hilbert and his students contributed significantly to establishing rigor and some tools to the mathematics used in modern physics. He is also known as one of the founders of proof theory , mathematical logic and the distinction between mathematics and metamathematics .

20. CONTRIBUTION OF MATHEMATICIANS TO MATHEMATICS BERNHARD RIEMANN Georg Friedrich Bernhard Riemann ( help · info ) (German pronunciation:  [ ˈriːman ] ; September 17, 1826 – July 20, 1866) was an influential German mathematician who made lasting contributions to analysis and differential geometry , some of them enabling the later development of general relativity .

21. CONTRIBUTION OF MATHEMATICIANS TO MATHEMATICS EUCLID Euclid of Alexandria , was a Greek mathematician and is often referred to as the “Father of Geometry.” He was active in Hellenistic Alexandria during the reign of Ptolemy I (323–283 BC). His Elements is the most successful textbook and one of the most influential works in the history of mathematics, serving as the main textbook for teaching mathematics (especially geometry) from the time of its publication until the late 19th or early 20th century. In it, the principles of what is now called Euclidean geometry were deduced from a small set of axioms. Euclid also wrote works on perspective, conic sections, spherical geometry, number theory and rigor.

22. CONCLUSION Thus the contributions of these mathematicians are tremendous in the field of mathematics. They gave a new era to the modern mathematics. Their methods are still around us and we are applying it. They gave some unique view to the world of mathematics which is unforgettable. If we compare of the situation under which they worked all and achieved this we come to realize that it is a great achievement for them.

23. BIBLIOGRAPHY Bourbaki , Nicolas (1998), Elements of the History of Mathematics , Berlin, Heidelberg, and New York: Springer- Verlag , 301 pages, ISBN   3-540-64767-8 . Boyer, C. B.; Merzback (fwd. by Isaac Asimov), U. C. (1991), History of Mathematics , New York: John Wiley and Sons, 736 pages, ISBN   0-471-54397-7 . Bronkhorst , Johannes (2001), "Panini and Euclid: Reflections on Indian Geometry", Journal of Indian Philosophy, (Springer Netherlands) 29 (1–2): 43–80, doi : 10.1023/A:1017506118885 . Burnett, Charles (2006), "The Semantics of Indian Numerals in Arabic, Greek and Latin", Journal of Indian Philosophy, (Springer-Netherlands) 34 (1–2): 15–30, doi : 10.1007/s10781-005-8153-z . Burton, David M. (1997), The History of Mathematics: An Introduction , The McGraw-Hill Companies, Inc., pp. 193–220. Cooke, Roger (2005), The History of Mathematics: A Brief Course , New York: Wiley- Interscience , 632 pages, ISBN   0-471-44459-6 . Dani , S. G. (25 July 2003), " Pythogorean Triples in the Sulvasutras " (PDF), Current Science 85 (2): 219–224. Datta , Bibhutibhusan (Dec 1931), "Early Literary Evidence of the Use of the Zero in India", The American Mathematical Monthly 38 (10): 566–572, doi : 10.2307/2301384 , JSTOR   2301384 .