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The computation of certain numbers using a ruler and compass. (English) Zbl 1010.11071
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.

MSC:
11Y60 Evaluation of number-theoretic constants
51M04 Elementary problems in Euclidean geometries
Software:
OEIS
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