- To give another interesting proof, we note that, if θ is an angle of any rational right triangle, sin θ and cos θ are rational and hence t = tan ½θ = sin θ/(1 + cos θ) is rational. Conversely, if t is rational, also are rational. The first mathematical article in this Monthly [1894, 6–11] was one on this subject by the present writer, who was co-editor of the Monthly from 1902 to 1908.
- The proof by Kronecker, Vorlesungen über Zahlentheorie, 1901, p. 35, is open to the serious objection raised by the writer in “Fallacies and misconceptions in Diophantine analysis,” Bulletin of the American Mathematical Society, April, 1921. Moreover, it is not proved that l is an integer.
- Comm. Arith. Coll., vol. 2, 1849, p. 648; Opera Postuma, vol. 1, 1862, p. 101.
- Journal für reine und angewandte Mathematik, vol. 37, 1848, pp. 1–20.
- L. E. Dickson, History of the Theory of Numbers, vol. 2, 1920, p. 639 seq.
The American Mathematical Monthly
Volume 28, 1921 - Issue 6-7