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Proofs of the mathematical result that the rational number 22 / 7 is greater than π (pi) date back to antiquity. One of these proofs, more recently developed but requiring only elementary techniques from calculus, has attracted attention in modern mathematics due to its mathematical elegance and its connections to the theory of Diophantine approximations.
The first few convergents (3, 22/7, 333/106, 355/113, ...) are among the best-known and most widely used historical approximations of π. Sequences of constants [ edit ]
is pi, the ratio of the circumference of a circle to its diameter. Euler's identity is named after the Swiss mathematician Leonhard Euler . It is a special case of Euler's formula e i x = cos x + i sin x {\displaystyle e^{ix}=\cos x+i\sin x} when evaluated for x = π {\displaystyle x=\pi } .
Super PI by Kanada Laboratory [102] in the University of Tokyo is the program for Microsoft Windows for runs from 16,000 to 33,550,000 digits. It can compute one million digits in 40 minutes, two million digits in 90 minutes and four million digits in 220 minutes on a Pentium 90 MHz. Super PI version 1.9 is available from Super PI 1.9 page.
Using Liu Hui's algorithm (which is based on the areas of regular polygons approximating a circle), Zu famously computed π to be between 3.1415926 and 3.1415927 [a] and gave two rational approximations of π, 22 / 7 and 355 / 113 , naming them respectively Yuelü (Chinese: 约率; pinyin: yuēlǜ; "approximate ratio") and Milü. [1]
The article is really about the number; the proof that it exceeds pi is interesting & notable because 22/7 is an important approximation of pi. It was suggested on the AfD debate that the article be renamed, and this seems like the best suggestion to me. Mangojuice 15:48, 20 March 2006 (UTC) Absolutely should be moved!
This category includes articles related to the mathematical constant pi (π), which represents the ratio of a circle's circumference to its diameter. For other uses, see Pi (disambiguation) . The main article for this category is Pi .
The Basel problem is a problem in mathematical analysis with relevance to number theory, concerning an infinite sum of inverse squares.It was first posed by Pietro Mengoli in 1650 and solved by Leonhard Euler in 1734, [1] and read on 5 December 1735 in The Saint Petersburg Academy of Sciences. [2]