[math-fun] GCD(1,π)

Consider GCD ring theoretically.  If a and b are elements of a ring R (which really should be an integral domain), GCD(a,b) is the smallest ideal in R containing a and b, and is the set of elements of the form ax + by as x and y range over R.  An ideal containing 1 can only be the entire ring.  If the ring is a field, then the only ideals are {0} and the entire field.  GCD(a,b) depends on the containing ring R.  If we take R to be the real numbers, then GCD(1,π) is R, which is also the ideal (a) for any nonzero a.  So one can let GCD(1,π) be any nonzero real number.   --  Gene