![]() ![]() Finding an accurate approximation of π (pi) has been one of the most important challenges in the history of mathematics. Infinite series for pi: In 1914, Ramanujan found a formula for infinite series for pi, which forms the basis of many algorithms used today. Ramanujan's contribution extends to mathematical fields such as complex analysis, number theory, infinite series, and continued fractions. Ramanujan’s major contributions to mathematics: In 1918, Ramanujan became the second Indian to be included as a Fellow of the Royal Society. He was mentored at Cambridge by GH Hardy, a well-known British mathematician who encouraged him to publish his findings in a number of papers. Srinivasa Ramanujan began developing his theories in mathematics and published his first paper in 1911. Rao was initially sceptical of Ramanujan, but he eventually recognised his abilities and supported him financially. Ramachandra Rao, secretary of the Indian Mathematical Society. He drifted through poverty until 1910 when he was interviewed by R. It was around this time that he began his famous notebooks. Another attempt at college in Madras (now Chennai) ended in failure when he failed his First Arts exam. He received a college scholarship in 1904, but he quickly lost it by failing in nonmathematical subjects. Despite being a mathematical prodigy, Ramanujan's career did not begin well. Every year, Ramanujan’s birth anniversary on December 22 is observed as National Mathematics Day.īorn in Erode, Tamil Nadu, India, Ramanujan demonstrated an exceptional intuitive grasp of mathematics at a young age. With its humble and sometimes difficult start, his life story is just as fascinating as his incredible work. Most of his mathematical discoveries were based only on intuition and were ultimately proven correct. Surprisingly, he never received any formal mathematics training. Leaving this world at the youthful age of 32, Ramanujan made significant contributions to mathematics that only a few others could match in their lifetime. \frac.Srinivasa Ramanujan (1887-1920), the man who reshaped twentieth-century mathematics with his various contributions in several mathematical domains, including mathematical analysis, infinite series, continued fractions, number theory, and game theory is recognized as one of history's greatest mathematicians. The common rational approximation of \pi, 22/7, has an infinitely long but repeating decimal expansion ( 3.142857142857\ldots), aside from being incorrect from the third decimal place onwards.Īround 1873, Shanks computed \pi to 707 decimal places, a record at the time, by employing an infinite series discovered by the astronomer John Machin , \pi is not a rational number, which means its decimal expansion is infinite in length, with no repeating pattern. Mathematically, Shanks’ \pi calculation can never end. However, his most accurate calculation would be that of \pi. Aside from having published a table of prime numbers up to 60,000, he computed highly accurate estimates-correct up to 137 decimal places-of the natural logarithms of 2, 3, 5, 7 and 10. William Shanks, a 19th century amateur British mathematician, had a flair for computation. This article explores this recently gained understanding of Ramanujan’s series, while also discussing alternative approaches to approximate \pi. And in the years preceding this computing feat, there were breakthroughs in understanding why Ramanujan’s series approximated \pi so well. However, these series were never employed for this purpose until 1985, when it was used to compute 17 million terms of the continued fraction of \pi. In 1914, he derived a set of infinite series that seemed to be the fastest way to approximate \pi. \pi, the all-pervading mathematical constant, has always fascinated mathematicians. ![]()
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |