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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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