Today I received my first unsolicited “proof” that it’s possible to square the circle. A footnote on the first page reads
An advise: If you strongly believe that (1) 3.1415926… is the value of π. (2) π is a transcendental number and (3) squaring of circle is impossible, you need not look at this work and waste your precious time.
Good advice… but curiosity got the better of me.
The author includes a few papers that he published in the IOSR journal of mathematics (a questionable publication, to put it mildly) in which he argues that π=(14-√2)/4 (≈ 3.1464466), which is of course algebraic, not transcendental, and that using this value for π it is possible to “square the circle”. He ends with some biographical information, including details and photos of family members and of sculptures that he has donated to various institutions.
To defend his assertion that π is not transcendental, he quotes a line from the chapter Quadrature of the Circle in Underwood Dudley’s Mathematical Cranks. Unfortunately, he fails to realise that the line he’s quoting is included as part of an example of the work of a crank.