355 / 113

355 / 113 = 3.141592.....

How would you -prove- that this is the best approximation of pi using only integers less than 1000 ? We can use a 'By Cases' / Brute Force approach and utilize a computer to go through all the possible quotients. Even going through a million of them is a piece of cake nowadays. I wonder if there is a computer-free approach. - Even with a computer its an interesting problem. I.e. what's the shortest program to prove it. The fastest? Go visit Project Euler and you'll be amazed what clever programmers can do in their favorite language. Even if, or especially if, you are a programmer yourself. Amaze yourself. Or take the challenge...