Pi = 4-4/3+4/5-4/7+4/9-4/11ā¦
Pi was proved by Lambert in 1761 to be irrational. (Think about it: it took thousands of years for someone to find a proof.) Lindemann proved in 1882 that pi is transcendental, a bigger deal. Oversimplified explanation: sqrt(2) is irrational but it can be constructed, as sqrt(2) is the hypotenuse of an isosceles right triangle with legs of length 1. (Some irrational numbers can be constructed.) Pi cannot be constructed with a compass and an unmarked straightedge. (Transcendental numbers cannot be constructed.)