Today I tagged along on the Google Intern Scavenger Hunt. But I am sworn to secrecy about on that topic. So I will not write about that. It wouldn't work to say, "Puzzle Hunts are Everywhere, including an undisclosed starting location" Thus, instead, this book report.
A few months ago, I started receiving envelopes of mail from India. The first few weren't signed, but the next few were. They were from Reddivari Sarva Jagannadha Reddy, sometimes known as R. S. J. Reddy. They were about geometry and Pi. They suggested that he'd found a proof that Pi is 3.1464466. I don't know why he sent me mail. Maybe he saw the Book report on Beckman's History of Pi? Maybe he saw my Python program for computing the value of Pi (slowly) by the Monte Carlo method? Neither of these things suggests that I am a Pi expert. (Indeed, I am not). I filed away the the mail with vague plans to look more closely "later."
Then the book arrived. The book by that same Reddivari Sarva Jagannadha Reddy, The untold story of THE TRUE VALUE OF π. OK, I'm not a mathematician. But maybe it was up to me to look at this book. And if this book had some merit, maybe I could bring it to someone's attention. Like, I could show it to a real mathematician and then they might say, "Hey, he's right, the accepted value of Pi has been off a little all these years."
So I went to a cafe, and ordered a big cup of coffee to excite whatever math-related neurons still survive in my brain. And I read. Now I was being very careful as I read because I'm not a mathematician and a lot of those fallacious-proof puzzles trip me up, and I didn't want to fall for a fallacious proof, but I didn't want to ignore a true proof. OK, so, coffee at the Blue Danube cafe on Clement Street, a nice spot to sit and read and draw circles and squares on a piece of paper.
As it turns out, I didn't need the coffee. The proof had a flaw. I was all set for something subtle. Mr. Reddy has spent years of his life developing this theory, so I figured if there was something wrong with it, it would have to be something that one could overlook for a few years. But it wasn't. Here is Reddy's proof:
[Draw a circle inscribed in a square; draw a sqare inscribed in the circle. These squares have different length sides. That difference is 2/6.8284275.] "It is clear from the diagram and deductions based on this the [difference between π and 3] one is forced to accept is 1/6.8284275."
My counterproof: It is not clear from the diagram. He describes the diagram. I drew the diagram. It is easy to see that he has found something close to π. But it is not clear that it is π.
The book contains several more "proofs." In each case, he "proves" that π is 3.1464466... if you accept that his original diagram correctly shows π. Or if you accept a new formula for the tangent function--based on his value for π. Of course, I can "prove" that π is equal to three if I'm allowed to use a tangent function which is based on the premise that π is three. I skimmed about ten of these proofs.
In his article "The Transcendental Number Pi," (collected in New Mathematical Diversions) Martin Gardner wrote
Early attempts to find an exact value for pi were closely linked with attempts to solve the classic problem of squaring the circle. ... Conversely, if the circle could be squared, a means would exist for constructing a line segment exactly equal to pi. However, there are ironclad proofs that pi is transcendental and that no straight line of transcendental length can be constructed with compass and straightedge.
It's too bad Gardner didn't provide any references to those ironclad proofs. Though I can look at Reddy's proof and say "Hey, that doesn't prove it", I don't have a real counter-proof.
Maybe RSJ Reddy sent me these proofs, not because I am a π expert, but because I am a non-expert π enthusiast? Perhaps he's had some luck winning such over in the past?
Looking at the author information, I saw that he was a Zoology teacher. Looking at the inside front cover of the book, I saw that he had another book, a theory of evolution, of "organic bloom". If this theory had as little foundation as his π theory, then I felt sorry for his students.
Still, it was a nice day to sit in a cafe. Mr Reddy had tricked me into wasting some time, but not much time. The coffee and music were good. If the worst problem in your life is that you're worried about some far-away Zoology students getting a bad education, your life is pretty easy.
Labels: book, crank, pi