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.

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