Книга: Proof That 22/7 Exceeds ?: Mathematical Proof, Rational Number, Pi, Diophantine Approximation, Continued Fraction, Decimal Representation, Archimedes, 3rd century BC, Perimeter

High Quality Content by WIKIPEDIA articles! Proofs of the famous mathematical result that the rational number 22?7 is greater than ? date back to antiquity. What follows is a one-line modern mathematical proof that 22?7 > ?, requiring only elementary techniques from calculus. The purpose is not primarily to convince the reader that 22?7 is indeed bigger than ? systematic methods of computing the value of ? exist. Unlike some elementary proofs, the calculus-based proof presented here is straightforward its elegance results from its connections to the theory of diophantine approximations. Stephen Lucas calls this proposition 'One of the more beautiful results related to approximating ?'. Julian Havil ends a discussion of continued fraction approximations of ? with the result, describing it as 'impossible to resist mentioning' in that context.