contribution of mathematicians.pdf
- 1. CONTRIBUTIONS OF GREAT MATHEMATICIANS Introduction The height which the mathematics is occupying today and the progress which it has made through the age is all due to the dedicated and sustained work of its great students. A large number of them have immortalized themselves by their memorable contribution to their subject. Mankind will remember them forever with gratitude. Their lives and deeds will continue to inspire the students and scholars. These were geniuses whose works will benefit the human race throughout its existence. Aryabhata Aryabhata was the first of the great Hindu Mathematicians. He lived from 475 A.D to 500 A.D in or near the present city of Patna. He wrote an arithmetic including under this heading arithmetic and geometric progressions, quadratic equations and indeterminate equations. He also computed arithmetical tables which contained a table of sines. His work in mensuration was crude and in this respect, it somewhat resembled that of the Egyptians. Contribution 1) Aryabhata invented a notation system consisting of alphabet numerals. Digits are denoted by alphabet numerals in this system. 2) Although earlier to Aryabhata, the method of extracting square root was evolved by Jain mathematicians, yet Aryabhata is known for giving its simple and clear explanation. 3) Aryabhata put more appropriate uses of the decimal system. 4) He gave almost all the formulae for knowing area of different figures like area of a square, rectangle, triangle, rhombus, circle and volumes of the spheres and cones etc. 5) He tried to point out the construction of different geometrical figures –triangle, quadrilateral, circle. 6) He for the first time in the world gave the value of 𝜋.
- 2. 7) He has given a method of addition, subtraction, division and multiplication of simple and compound algebraic quantities (integer as well as fractional). He mentioned the algebraic formulae like (𝑎 + 𝑏)2 = 𝑎2 + 2𝑎𝑏 + 𝑏2 𝑎𝑛𝑑 𝑎𝑏 = (𝑎+𝑏)2−(𝑎2+𝑏2) 2 . 8) He tried to give a rule for summing an arithmetic series after p th term. 9) He tried to solve indeterminate linear equations like 𝑎𝑥 ± 𝑏𝑦 = 𝑐 𝑏𝑦 𝑡ℎ𝑒 𝑚𝑒𝑡ℎ𝑜𝑑 of the fractions which is substantially the same as the method in use today. 10)His contribution in geometry are commendable. Also famous Pythagoras theorem seen different form in his work. 11)Aryabhata paid considerable attention to trigonometry and his introduction of sines was a noteable improvement upon the clumsy half-chords of Ptolemy. 12)Aryabhata in addition to mathematics was also the master of astronomy. C.F.Gauss Carl Friedrich Gauss was born at Brunswick, Germany. He is a famous Astronomer, Physicist and a Mathematician. Every work Gauss produced was an event in history of Mathematics and sciences and hence he lives everywhere in mathematics and sciences. Contributions 1) At the age of 19 years on 30 th March, 1796 he invented the process of constructing a polygon of 17 sides with the help of a ruler and compass only. 2) In 1799 his first book ‘Disquisitions Arithmeticae was published. It brought the following things into time light: - I. Proofs of the following algebraic facts were first seen in this book. a. Every integral rational equation in a single variable has atleast one root. b. Every equation will have as many roots as the highest power of the unknown. II. He presented a total picture of the number system through this book. Besides negative, positive, rational and irrational numbers he firmly dealt with imaginary numbers. III. He for the first time, used the symbol ‘ⅈ’ for expressing imaginary quantity √−1. 𝑇ℎ𝑒 𝑛𝑢𝑚𝑏𝑒𝑟𝑠 𝑙𝑖𝑘𝑒 4 + 2√−1 or 4 + 2ⅈ were named as complex
- 3. number by him and he introduced the world with the characteristic of such numbers 3) He brought something new in the calendar system by becoming successful to know the exact date of Easter and his birthday. 4) At the age of 24 he turned towards astronomy. He computed accurately the orbits of some newly discovered planet and satellites. 5) He spent the valuable ten years of his life in Geodetic researches. He did so many researches in the subjects Differential geometry, Theory of surfaces, Statistics etc. In the theory of probability, he was the originator of the famous law “Gaussian Law of Normal Distribution of Errors”. 6) He was a Master of Mathematics of motions and growth that had been developed by Newton and Leibnitz, so much so that he shares with Lagrange and Laplace a foremost place among the founders of modern mathematical analysis. 7) He was one of the first to the study what is known as the non Euclidean geometry that is now associated with the name of Nikolas Ivano Vitch Lobachivsky of the University of Kazan. 8) Three of the problems which Gauss considered in his work on surfaces suggested general theories of mathematical and scientific importance. The method Gauss invented in the branches like measurement of curvature, the theory of conformal mapping and the applicability of surfaces were general and of wide utility. 9) Gauss won lasting fame for his scientific researches into magnetism and electricity. In this connection he demonstrated the possibility of sending telegraphic signals from Gottingen to a neighbouring town and thus played a part in developing the ideas on which such famous scientists as Galvani Volta and Ampere had been working.