Summary: We present a method for computing some numbers bit by bit using only a ruler and compass, and illustrate it by applying it to $arctan(X)/Pi$. The method is a spigot algorithm and can be applied to numbers that are constructible over the unit circle and the ellipse. The method is precise enough to produce about 20 bits of a number, that is, 6 decimal digits in a matter of minutes. This is surprising, since we do no actual calculations.