Ramanuja maths

Not to be confused with In Ramanujan's sum, usually denoted c q( n), is a function of two positive integer variables q and n defined by the formula c q ( n ) = ∑ 1 ≤ a ≤ q ( a , q ) = 1 e 2 π i a q n , See also [ ] • • Notes [ ] • Ramanujan, On Certain Trigonometric Sums ... These sums are obviously of great interest, and a few of their properties have been discussed already. But, so far as I know, they have never been considered from the point of view which I adopt in this paper; and I believe that all the results which it contains are new.( Papers, p. 179). In a footnote cites pp. 360–370 of the Dirichlet–Dedekind Vorlesungen über Zahlentheorie, 4th ed. • Nathanson, ch. 8. • Hardy & Wright, Thms 65, 66 • G. H. Hardy, P. V. Seshu Aiyar, & B. M. Wilson, notes to On certain trigonometrical sums ..., Ramanujan, Papers, p. 343 • Schwarz & Spilken (1994) p.16 • B. Berndt, commentary to On certain trigonometrical sums..., Ramanujan, Papers, p. 371 • Knopfmacher, p. 196 • Hardy & Wright, p. 243 • Tóth, external links, eq. 6 • Tóth, external links, eq. 17. • Tóth, external links, eq. 8. • B. Berndt, commentary to On certain trigonometrical sums..., Ramanujan, Papers, pp. 369–371 • Ramanujan, On certain trigonometrical sums... The majority of my formulae are "elementary" in the technical sense of the word — they can (that is to say) be proved by a combination of processes involving only finite algebra and simple general theorems concerning infinite series( Papers, p. 179) • The t...

• Full Name: Srinivasa Aiyangar Ramanujan • Known For: Prolific mathematician • Parents’ Names: K. Srinivasa Aiyangar, Komalatammal • Born: December 22, 1887 in Erode, India • Died: April 26, 1920 at age 32 in Kumbakonam, India • Spouse: Janakiammal • Interesting Fact: Ramanujan's life is depicted in a book published in 1991 and a 2015 biographical film, both titled "The Man Who Knew Infinity." Early Life and Education Ramanujan was born on December 22, 1887, in Erode, a city in southern India. His father, K. Srinivasa Aiyangar, was an accountant, and his mother Komalatammal was the daughter of a city official. Though Ramanujan’s family was of the However, it was G.S. Carr’s book, "A Synopsis of Elementary Results in Pure Mathematics," which reportedly spurred Ramanujan to become obsessed with the subject. Having no access to other books, Ramanujan taught himself mathematics using Carr’s book, whose topics included integral calculus and power series calculations. This concise book would have an unfortunate impact on the way Ramanujan wrote down his mathematical results later, as his writings included too few details for many people to understand how he arrived at his results. Ramanujan was so interested in studying mathematics that his formal education effectively came to a standstill. At the age of 16, Ramanujan matriculated at the Government College in Kumbakonam on a scholarship, but lost his scholarship the next year because he had neglected his other studies. He then ...

Biography Srinivasa Ramanujan was one of India's greatest mathematical geniuses. He made substantial contributions to the analytical theory of numbers and worked on Ramanujan was born in his grandmother's house in Erode, a small village about 400 km southwest of Madras (now Chennai ). When Ramanujan was a year old his mother took him to the town of Kumbakonam, about 160 km nearer Madras. His father worked in Kumbakonam as a clerk in a cloth merchant's shop. In December 1889 he contracted smallpox. When he was nearly five years old, Ramanujan entered the primary school in Kumbakonam although he would attend several different primary schools before entering the Town High School in Kumbakonam in January 1898. At the Town High School, Ramanujan was to do well in all his school subjects and showed himself an able all round scholar. In 1900 he began to work on his own on mathematics summing geometric and arithmetic series. Ramanujan was shown how to solve 1902 and he went on to find his own method to solve the (and of course failed ) to solve the quintic. It was in the Town High School that Ramanujan came across a mathematics book by G S Carr called Synopsis of elementary results in pure mathematics. This book, with its very concise style, allowed Ramanujan to teach himself mathematics, but the style of the book was to have a rather unfortunate effect on the way Ramanujan was later to write down mathematics since it provided the only model that he had of written mathematical arg...

In modern basic recreational mathematics, a magic square of order n numbers, usually different integers, in a square, such that the n numbers in all rows, all columns, and both diagonals sum to the same positive number. A trivial magic square contains the integers from 1 to. But in Ramanujan Magic Square the unique thing is the numbers on the topmost layers is his birthday: “22/12/1887.” Here in this article, will show you how to make a magic square out of your own birthdate. Check the main reasons what is unique about ramanujan magic square. Srinivasa Ramanujan was an Indian mathematician. He had almost no formal experience in mathematics but made upheld contributions to theoretical mathematics, number theory, infinite series, and continued fractions. When he was 11 and half years old, someone gave him a book on trigonometry, and he learned by himself. Ramanujan Magic Square In his teenage years, a friend of his family gave him a math encyclopedia with around 7,000 theorems. That was all the math training he had, where today’s kid passed the class 10 th examination. At age 23, Ramanujan generated a formula that would calculate all primes up to 100,000,000. He then was invited to move to Cambridge city and there he proved or conjectured over 3,000 results, including the best algorithms we have to this day for generating the digits of. Check: Seeing his enchantment square made me intrigued into making my own birthday sorcery square. My birthday is September 24, 1998, so tha...

Ramanujan's manuscript. The representations of 1729 as the sum of two cubes appear in the bottom right corner. The equation expressing the near counter examples to Fermat's last theorem appears further up: α 3 + β 3 = γ 3 + (-1) n. Image courtesy A box of manuscripts and three notebooks. That's all that's left of the work of Srinivasa Ramanujan, an Indian mathematician who lived his remarkable but short life around the beginning of the twentieth century. Yet, that small stash of mathematical legacy still yields surprises. Two mathematicians of Emory University, Ramanujan's story is as inspiring as it is tragic. Born in 1887 in a small village around 400 km from Madras (now Chennai), Ramanujan developed a passion for mathematics at a young age, but had to pursue it mostly alone and in poverty. Until, in 1913, he decided to write a letter to the famous Cambridge number theorist The taxi-cab number The romanticism rubbed off on the number 1729, which plays a central role in the Hardy-Ramanujan story. "I remember once going to see [Ramanujan] when he was ill at Putney," Hardy wrote later. "I had ridden in taxi cab number 1729 and remarked that the number seemed to me rather a dull one, and that I hoped it was not an unfavourable omen. 'No', he replied, 'it is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways.'" What Ramanujan meant is that The anecdote gained the number 1729 fame in mathematical circles, but until re...