==> analysis/irrational.stamp.s <==
Yes. Center the stamp at (0,0), (1,0), and (0,pi).
Suppose there is a point (x,y) which is not covered.
Then there are rational numbers a,b,c satisfying the following equations:
(1) x^2 + y^2 = a
(2) (x-1)^2 + y^2 = b
(3) x^2 + (y-pi)^2 = c
Subtract (2) from (1) and solve for x. Thus x is rational.
From equation (2), y is algebraic. But equation (3) implies
that y is transcendental, contradiction.