Plouffe, Simon The computation of certain numbers using a ruler and compass. (English) Zbl 1010.11071 J. Integer Seq. 1, Art. 98.1.3. (1998). 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. Cited in 1 Document MSC: 11Y60 Evaluation of number-theoretic constants 51M04 Elementary problems in Euclidean geometries Software:OEIS PDF BibTeX XML Cite \textit{S. Plouffe}, J. Integer Seq. 1, Art. 98.1.3. (1998; Zbl 1010.11071) Full Text: EuDML EMIS Online Encyclopedia of Integer Sequences: Positions of ones in binary expansion of arctan(1/2)/Pi. Binary expansion of arctan(1/2)/Pi. a(n) = 5^n*sin(2n*arctan(1/2)) or numerator of tan(2n*arctan(1/2)). a(n) = 5^n*cos(2*n*arctan(1/2)) or denominator of tan(2*n*arctan(1/2)). Imaginary part of (5+12i)^n. Real part of (5 + 12i)^n. a(n) = 17^n sin(2n arctan(1/4)) or numerator of tan(2n arctan(1/4)). a(n) = 17^n*cos(2*n*arctan(1/4)) or denominator of tan(2*n*arctan(1/4)). Decimal expansion of arctan(1/2)/Pi.