A couple of weeks ago I posted pictures of a letter that I received from one R.S.J. Reddy claiming that the exact value of of $latex pi$ was $latex frac{14-sqrt{2}}{4}$ which equals 3.1464466… and I asked all of you wonderful readers, and listeners, to help me find out where he went wrong. Well, you all came through and what follows is a a general consesus of where the work of R.S.J. Reddy left the rails.
The letter itself contained 3 methods that Reddy used to derive his new value of $latex pi$, the Siva Method, the jesus Method, and the Hippocrates method, but before we tackle how those methods incorrectly derived the value of $latex pi$ I am going to mention a couple of general problems with this value.
General Mistakes
The first general mistake comes from Colin W.(@ColinTheMathmo on twitter where he sent this to me) who mentioned that the new value of $latex pi$ just happens to violate the work of Archimedes who proved long ago that the circle constant has to occur between $latex 3 frac{10}{71}approx 3.14084dots$ and $latex 3 frac{1}{7}approx 3.14285dots$. If that is not enough both Stephen M. and Steve W.(@swildstorm) chipped in with the problem that $latex frac{14-sqrt{2}}{4}$ happens to be an algebraic, not transcendental, violating Lindemann’s proof that $latex pi$ is not a root of a non-constant polynomial equation with rational coefficients as $latex frac{14-sqrt{2}}{4}$ is a root of the polynomial $latex 2x^{2}-14x+frac{97}{4}=0$.
