In 1706 mathematician William Jones, born
in the small village of Llanfihangel Tre'r Beirdd
on Anglesey, became the first person to use the
16th letter of the Greek alphabet to represent
the ratio of the circumference of a circle to
its diameter. Previously the ratio was known as
the Ludolphian number, after Ludolph van Ceulen,
a German mathematician. 

We all know that $\pi$ can be approximated as 22/7, but
did you know that a better approximation is $\frac{355}{113}$ ?
That's better than one part in 10 million, which seems
unreasonably good.
Questions:
 Where does that come from?
 Can every number be approximated?
 Why are some numbers better approximated than others?
 Are there any with especially bad approximations?
See also
Proof By Contradiction.
CategoryMaths