Monday, July 23, 2012

Numerical Approximations and Debunking the Claim that π has an exact value


I apologize for not blogging sooner (getting over a nasty sore throat/cold). I am still working on the application series, planning to get that started on or before August 1, 2010.

Numerical Approximations

In the meantime, I am also reading about a series of numerical analysis by Namir Shammas. Please click here to go to his web page. . I am really fascinated about his paper on integration methods and polynomials he uses to better fit data.

There is also a paper on inverse distribution which can come in handy for those in statistics and probability. For example, the inverse normal distribution lets you find the z-point given the α, the level of significance. So, if the given area under the normal curve is .95, α = .05.

Is There an Exact Value for π? One Man Thinks So (He Isn't Correct)

There is this mathematician from India who claimed to have found an exact value for π, which the claimed value was well off from the true value of 3.14159265359... (off by at least .005). The way he found his value for π was by a Sieve method, which was a very confusing method involving dissecting an circle inscribed in a square, and balancing areas of circular sectors inside and outside the inscribed circle. Problem was he made an assumed value for π to conclude some convenient number. I did not get into his other two methods.

Here is the article where the errors are posted, published by Acme Science, a blog authored by Samuel Hansen (Twitter: @Samuel_Hansen): please click here.

I hope your days are well and without sickness. You can follow me on Twitter: @edward_shore. Until next time,


1 comment:

  1. I forget where I read about it, but someone wrote a program to generate simple fractions (like the famous 22/7 one) that give values close to π. He found that the number of significant digits in the fraction was the same, +/- 1, as the number of *correct* digits in the π approxomation. So, 22/7 with its 2 significant digits, is one of the better approximations, giving one more digit of π than goes into it.

    The main point I got from this is that there still ain't no free lunch. There may be some solid number-theoretical reason for this.


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