INDIAN MATHEMATICIAN

1. Aryabhata (475 A.D.-550 A.D.)
   
   Aryabhata is the first well known Indian mathematician.
   Born in Kerala, he completed his studies at the university of Nalanda.
   In the section Ganita (calculations) of his astronomical treatise Aryabhatiya (499 A.D.), he made the fundamental advance in finding the lengths of chords of circles,by using the half chord rather than the full chord method used by Greeks.He gave the value of pi as 3.1416, claiming, for the first time,that it was an approximation.(He gave it in the form that the approximate circumference of a circle of diameter 20000 is 62832.) He also gave methods for extracting square roots,summing arithmetic series, solving indeterminate equations of the type ax -by = c,and also gave what later came to be known as the table of Sines.He also wrote a text book for astronomical calculations, Aryabhatasiddhanta.Even today, this data is used in preparing Hindu calendars (Panchangs). In recognition to his contributions to astronomy and mathematics, India's first satellite was named Aryabhata.


2. Brahmagupta (598 A.D. -665 A.D.)
   Brahmagupta is renowned for introduction of negative numbers and operations on zero into arithmetic. His main work was Brahmasphutasiddhanta, which was a corrected version of old astronomical treatise Brahmasiddhanta. This work was later translated into Arabic as Sind Hind. He formulated the rule of three and proposed rules for the solution of quadratic and simultaneous equations. He gave the formula for the area of a cyclic quadrilateral. He was the first mathematician to treat algebra and arithmetic as two different branches of mathematics. He gave the solution of the indeterminate equation Nx²+1 = y². He is also the founder of the branch of higher mathematics known as "Numerical Analysis".


3. Bhaskara (1114 A.D. -1185 A.D.)
   Bhaskara (1114 A.D. -1185 A.D.) or Bhaskaracharaya is the most well known ancient Indian mathematician. He was born in 1114 A.D. at Bijjada Bida (Bijapur,Karnataka) in the Sahyadari Hills. He was the first to declare that any number divided by zero is infinity and that the sum of any number and infinity is also infinity. He is famous for his book Siddhanta Siromani (1150 A.D.). It is divided into four sections -Leelavati (a book on arithmetic), Bijaganita (algebra), Goladhayaya (chapter on sphere -celestial globe), and Grahaganita (mathematics of the planets).Leelavati contains many interesting problems and was a very popular text book.Bhaskara introduced chakrawal, or the cyclic method, to solve algebraic equations.Six centuries later, European mathematicians like Galois, Euler and Lagrange rediscovered this method and called it "inverse cyclic". Bhaskara can also be called the founder of differential calculus. He gave an example of what is now called "differential coefficient" and the basic idea of what is now called "Rolle's theorem".Unfortunately, later Indian mathematicians did not take any notice of this. Five centuries later, Newton and Leibniz developed this subject. As an astronomer,Bhaskara is renowned for his concept of Tatkalikagati (instantaneous motion).


4. Mādhava of Sañgamāgrama (c. 1350 – c. 1425)
   Mādhava of was a prominent Kerala mathematician-astronomer from the town of Irińńālakkuţa near Cochin, Kerala, India. He is considered the founder of the Kerala School of Astronomy and Mathematics. He was the first to have developed infinite series approximations for a range of trigonometric functions, which has been called the "decisive step onward from the finite procedures of ancient mathematics to treat their limit-passage to infinity". His discoveries opened the doors to what has today come to be known as Mathematical Analysis. One of the greatest mathematician-astronomers of the Middle Ages, Mādhavan made pioneering contributions to the study of infinite series, calculus, trigonometry, geometry and algebra.Among his many contributions, he discovered the infinite series for the trigonometric functions of sine, cosine, tangent and arctangent, and many methods for calculating the circumference of a circle. One of Madhava's series is known from the text Yuktibhāṣā, which contains the derivation and proof of the power series for inverse tangent, discovered by Madhava.Madhava also gave a most accurate table of sines, defined in terms of the values of the half-sine chords for twenty-four arcs drawn at equal intervals in a quarter of a given circle.Madhava also carried out investigations into other series for arclengths and the associated approximations to rational fractions of π, found methods of polynomial expansion, discovered tests of convergence of infinite series, and the analysis of infinite continued fractions. He also discovered the solutions of transcendental equations by iteration, and found the approximation of transcendental numbers by continued fractions.Madhava laid the foundations for the development of calculus, which were further developed by his successors at the Kerala school of astronomy and mathematics. (It should be noted that certain ideas of calculus were known to earlier mathematicians.) Madhava also extended some results found in earlier works, including those of BhāskaraII.


5. Ramchundra (Ramachandra Lal)(1821 – 1880)
   Ramchundra (Ramachandra Lal) was British India's first major mathematician. His book, Treatise on Problems of Maxima and Minima, was promoted by the prominent mathematician Augustus De Morgan.De Morgan, in his Introduction to Ramchundra's book says that he was born in 1821 in Panipat to Sunder Lal,a Kayasth of Delhi. De Morgan came to know of Ramchundra when, in 1850, he was sent by a friend a work on maxima and minima by the 29-year old self-taught mathematician. Ramchundra had published his book at his own expense in Calcutta in that year. De Morgan arranged for the book to be republished in London under his own supervision.De Morgan was so impressed that he undertook to bring Ramchundra's work to the notice of scientific men of Europe.Charles Muses, in an article in the Mathematical Intelligencer (1998) called Ramchundra "De Morgan's Ramanujan". He was mystified why, in spite of De Morgan's efforts to make this "remarkable Hindu algebraist known, he does not appear in most texts on history of mathematics."Ramchundra was teacher of science in Delhi College for some time. In 1858, he was native head master in Thomason Civil Engineering College (now Indian Institute of Technology, Roorkee) at Roorkee. Later that year, he was appointed head master of a school in Delhi.


6. Srinivasa Aaiyangar Ramanujan(22 december 1887 – 26 april 1920)
   Srinivasa Aaiyangar Ramanujan is undoubtedly the most celebrated Indian Mathematical genius. He was born in a poor family at Erode in Tamil Nadu on December22,1887.Largely self taught, he feasted on Loney's Trigonometry at the age of 13, and at the age of 15, his senior friends gave him Synopsis of ElementaryResults in Pure and Applied Mathematics by George Carr. He used to write his ideas and results on loose sheets. His three filled notebooks are now famous as Ramanujan's Frayed Notebooks. Though he had no qualifying degree, the University of Madras granted him a monthly scholarship of Rs. 75 in 1913. A few months earlier, he had sent a letter to great mathematician G.H. Hardy, in which he mentioned 120 theorems and formulae. Hardy and his colleague at Cambridge
   University, J.E. Littlewood immediately recognised his genius. Ramanujan sailed for Britain on March 17, 1914. Between 1914 and 1917, Ramanujan published 21 papers, some in collaboration with Hardy. His achievements include Hardy-Ramanujan-Littlewood circle method in number theory, Roger-Ramanujan's identities in partition of numbers, work on algebra of inequalities, elliptic functions,continued fractions, partial sums and products of hypergeometric series, etc. He was the second Indian to be elected Fellow of the Royal Society in February, 1918. Later that year, he became the first Indian to be elected Fellow of Trinity College,Cambridge. Ramanujan had an intimate familiarity with numbers. During an illness in England, Hardy visited Ramanujan in the hospital. When Hardy remarked that he had taken taxi number 1729, a singularly unexceptional number, Ramanujan immediately responded that this number was actually quite remarkable: it is the smallest integer that can be represented in two ways by the sum of two cubes: 1729=1³+12³=9³+10³. Unfortunately, Ramanujan's health deteriorated due to tuberculosis, and he returnted to India in 1919. He died in Madras on April 26, 1920.

NUMBER MAGIC

1. 111/(1+1+1)=37
   222/(2+2+2)=37
   333/(3+3+3)=37
   444/(4+4+4)=37
   555/(5+5+5)=37
   666/(6+6+6)=37
   777/(7+7+7)=37
   888/(8+8+8)=37
   999/(9+9+9)=37


2. The Magic Number 1089:
   
   • Use your first piece of paper to write down the number "1089". After you write down the number, ball it up and place it on the floor.
   
   
   • Use your first piece of paper to write down the number "1089". After you write down the number, ball it up and place it on the floor.
   
   
   • Tell your friend to reverse the digits.For example, 742 is reversed to 247. Next, tell your friend to subtract the bigger number and the smaller number.
   
   
   • Tell your friend to reverse the answer he just got. After that, your friend should add up the last two digits.
   
   
   • Your friend should come up with a total of 1089. Ask your friend the answer he/she got. When he/she tells you the answer, grab the piece of paper that you had on the floor. Unball the piece of paper and show your friend.
   
   
   • Your friend will be amazed!
   
   
   
   Examples: A. 753 - 357 = 396 B. 396 + 693 = 1089 A. 846 - 648 = 198 B. 198 + 891 = 1089 As you can see, the answer will always be 1089
   


3. If you multiply the number 142,857 by anything between 1 and 6
   
   the answer contains the same digits.
   
   e.g. 142857 x 3 = 428571 and 142857 x 6 = 857142
   
   If you multiply the same figure by 7 the answer is 999,999.