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:<math>\pi \approx 3.141592\dots\,</math>
 
Nel seguito si dimostrerà che 22/7 è maggiore di pi greco per via puramente analitica.
 
==The L'idea==
Although many people know this numerical value of &pi; from school, far fewer know how it is computed. What follows is a [[mathematical proof]] that 22/7 > &pi;. It is ''simple'' in that it is short and straightforward, and requires only an elementary understanding of [[calculus]].
 
==The idea==
 
:<math>0<\int_0^1\frac{x^4(1-x)^4}{1+x^2}\,dx=\frac{22}{7}-\pi.</math>
 
ThereforeQuindi 22/7 > &pi;.
 
==TheI detailsdettagli==
 
That the [[integral]] is positive follows from the fact that the [[integrand]] is a quotient whose numerator and denominator are both nonnegative, being sums or products of even powers of [[real numbers]]. So the integral from 0 to 1 is positive.
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