#continuedfractions

[lionmageaz]

So today I started testing out some continued fraction code I'm adding to my little math project. I implemented π as a sum of rationals that only gets calculated on a term-by-term basis, then decided to pit it against my tried-and-true π implementation that uses the BBP algorithm.

ContinuedFraction picf = ContinuedFraction.pi(MathContext.DECIMAL128) println picf println picf.asBigDecimal().toPlainString() Pi pi = Pi.getInstance(MathContext.DECIMAL128) println pi println pi.asBigDecimal().toPlainString() [3; 7, 15, 1, 292, 1, 1, 1, 1, 1, 1, 12, 3931, 1, 18, 9, 1, 1, 1, 1, …] Dec 25, 2024 12:28:29 AM tungsten.types.numerics.impl.ContinuedFraction$1 apply INFO: Cannot find term 34 in cache; iterating over 14 terms and caching. 3.141592653572765844350521157053832 𝜋[34] 3.141592653589793238462643383279503

The continued fraction has 8 accurate terms, and its decimal representation is accurate to 11 digits. Not too bad!

[pixoplanet]

It's December 22nd, 🧮 National Mathematics Day in India. On this day in 1887, the brilliant mathematician Srinivasa Ramanujan was born in Erode, Tamil Nadu. Ramanujan was responsible for advances in number theory, infinite series, and continued fractions, including solutions to mathematical problems until then considered unsolvable. Schools and universities throughout India celebrate his birthday now with math contests, games, demonstrations, and other educational events. In 2017, the day’s significance was enhanced by the opening of the Ramanujan Math Park in Kuppam, Chittoor, Andhra Pradesh.

Ramunajan's genius was obvious from childhood. By the age of 12, he had mastered trigonometry and developed many of his own theorems. Ramanujan’s peers at the time said they rarely understood him and stood in respectful awe of him, but his ideas were too novel for the leading mathematicians in India to be bothered with.

In 1913, when Ramanujan was 25, British mathematician G.H. Hardy became enamored with his theorems and got him into Cambridge University. Ramanujan thrived in Britain and was soon elected to be a member of the London Mathematical Society. In 1918, at the age of 30, he became a Fellow of the Royal Society – one of the youngest persons to ever achieve this esteemed position.

Ramanujan returned to India in 1919 because the food in Britain didn't agree with him. His health continued to deteriorate, and he died in 1920 at the tender age of 32. His achievements in mathematics, however, continue to live on and grow ever larger. His notebooks of unpublished material are a source of new ideas to this day. Of his thousands of theorems, all but a dozen or so have by now been proven correct. A century after his death, researchers are still discovering that mere comments in his writings about "simple properties" and "similar outputs" were themselves profound and subtle number theory results.

It's no wonder that in 2012, former Prime Minister of India Manmohan Singh declared Ramanujan’s birthday as National Mathematics Day to be celebrated across the country. ☮️ R.I.P., Mr. Ramanujan… Jamiese of Pixoplanet

[blogofhistory-blog1]

Birth Anniversary..! Srinivasa Ramanujan..! 22 December 1887..! #SrinivasaRamanujan was an #Indian #Mathematician who lived during the #BritishRule in #India..! Though he had almost no formal training in pure mathematics, he made substantial contributions to #MathematicalAnalysis, #NumberTheory, #InfiniteSeries, and #ContinuedFractions, including solutions to #MathematicalProblems considered to be unsolvable..! https://www.instagram.com/p/BrqXtVAgckAmDEQkSkMAZ_ndhlkgbcUc951ikM0/?utm_source=ig_tumblr_share&igshid=supuvdghhl0s