# The irrationality of Pi [duplicate]

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?

• Irrational numbers cannot be expressed as a fraction of integers. Thus, a circle cannot have a diameter and circumference which are both integers. Commented Nov 10, 2015 at 17:29
• In practice this is no problem because we can use arbitary good rational approximations of $\pi$, a very good one is $\frac{355}{113}$ Commented Nov 10, 2015 at 17:30
• Archimedes was the first to calculate $\pi$ upto some digits. Commented Nov 10, 2015 at 17:31
• He approximated the circumfence of a circle with regular polygons inside ans outside the circle and took the middle value of the results. Commented Nov 10, 2015 at 17:33
• The definition is usually : The first positive root of $cos(x)$ is $\frac{\pi}{2}$ Commented Nov 10, 2015 at 17:35