355/113

The fraction 355/113 is incredibly close to pi, within a third of a millionth of the exact value. This level of accuracy is far beyond its rights as a fraction with such a small denominator, and it causes various oddities elsewhere in math. For example, use any scientific calculator to compute cos(355) in radians. The oddball result is due to the freakish closeness of 355/113 to pi.

– http://davidbau.com/archives/2010/03/14/the_mystery_of_355113.html