# Error Spotted, actually errors spotted.

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\$.

# Spot the Error

This past Monday I recieved a surprise piece of mail from India. Once I got over my initial shock of getting a piece of personal mail, an event that has not happened in a long time, I quickly found that this piece of mail contained other surprises as well. First of all it was addressed to a Dr. Samuel Hansen, a title that I will accept but have in no way earned. My next surprise came when I opened it an found that it was a letter claiming that the author, a R. Sarva Jagannadha Reddy, had discovered the exact value of pi. This seemed to me to be a rather surprising claim, but I was willing to go along with it until I flipped the page and found that the claimed exact value of pi was \$latex frac{14-sqrt{2}}{4}\$ which equals 3.1464466…..

I found it somewhat improbable that the best mathematical minds in history had made a mistake on the thousandths digit of one of the most important and used constants in the world. So of course I did some quick googling to see if I could find out any more information about RSJ Reddy and, too my complete lack of surprise, I found out that I was not the first person to recieve this letter(apparently he will eventually send you a whole book about he value of pi). The one thing that I did not find was a complete takedown of the work. I am currently very busy working on Relatively Prime, and while crank baiting is fun it is not as important, so I was hoping that I could enlist the help of ACMEScience community for this project. Under this post I will include photos of every page of the letter and I want everyone to look through the mathematics and figure out where it goes off the rails and explain the where and how in the comment section below. Once all of the errors have been identified I will collect them together in a blog post. Remember this is a public service, when the next person receives this letter and goes to google, we want to make sure there is a clear explanation of just why it is complete, and utter, bug splat on the windshield of mathematics.