This problem appeared in the Science and Technology section of Cumhuriyet on Friday, 10 April 2009 (click image for the question). I confess I wasn't able to solve this problem unaided; I had to look up le théorème d'Al-Kashi. (Jamshid al-Kashi gets a mention in the article on approximations of pi for having derived, in 1424, 9 digits of 2π in base 60.)