On Proofs of the Irrationality of √2

Abstract

In This paper there are given thirteen proofs that √2 is irrational. Indications are given as to whether the method employed extends to proving the irrationality of other square roots or of roots of higher order. In addition, a reference is provided to an incorrect proof recently published and its criticism.

Non-P-recursiveness of numbers of matchings or linear chord diagrams with many crossings

“…Irrationality of √ 2 via decimals? Many proofs of irrationality of the number √ 2 were published and collected, e.g., Beigel [4], Bogomolny [5] (at least 19 on-line proofs), Flannery [16], Gardner [19] (lists 18 references), Harris [24] (13 proofs), Miller and Montague [32], Myerson [33], Subbarao [42], and Waterhouse [44], and many textbooks on algebra, mathematical analysis and number theory present such proof: Allouche and Shallit [1, Theorem 2.2.1], Apostol [2, Theorem 1.10], Hardy and Wright [23,Theorem 43], Jarník [26, str. 16], Pugh [34, p. 11], Tao [43,Proposition 4.4.4], Zorich [45,p.…”