Consider 2 integers such that $a/b \approx\pi$. Let $c=|\pi-(a/b)|$ As $a$ and $b$ grow $c \to 0$. Now consider $d=abc$. Do $a$ and $b$ exist such that $d$ is less than it would be for any other pair?
optimal solution for rational PI approximation
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number-theory
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0so you want to know if there exist such $a$ and $b$ so that $d$ is smallest for every other pair? – 2012-10-08
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0smallest value would be so that $a/b=\pi$,except when either $a$ or $b$ is negative,in such case smallest would be negative infinite – 2012-10-08
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0dato, if $a,b$ are integers, then $a/b=\pi$ is impossible. – 2012-10-08
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0aaaa yes i missed – 2012-10-08