The irrationality of Pi [duplicate]

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Pi is defined as circumference/diameter, but it is an irrational number. And by definition an irrational number can't be defined by a fraction. So how is it that pi is circumference/diameter and on a side note: how are important irrational numbers like e normally found?

marked as duplicate by MJD, Eric Wofsey, ncmathsadist, user99914, BLAZENov 11 '15 at 3:58

• In practice this is no problem because we can use arbitary good rational approximations of $\pi$, a very good one is $\frac{355}{113}$ – Peter Nov 10 '15 at 17:30
• Archimedes was the first to calculate $\pi$ upto some digits. – Peter Nov 10 '15 at 17:31
• The definition is usually : The first positive root of $cos(x)$ is $\frac{\pi}{2}$ – Peter Nov 10 '15 at 17:35